When estimating the amount of paint needed, Janice should strive for an accurate estimate to avoid running out of paint or wasting excess. Factors to consider include the size of the apartment, the type of paint, and the need for multiple coats.
Explanation:When estimating the amount of paint needed, Janice should strive for an accurate estimate to avoid running out of paint or wasting excess. Since the store sells paint in one-gallon cans, it is best to estimate in whole gallons. However, if Janice wants a more precise estimate, she can consider the following factors:
The size of the apartment: She can measure the walls and ceiling to calculate the surface area that needs to be painted.The type of paint: Different surfaces require different amounts of paint. For example, a textured wall may require more paint than a smooth wall.Multiple coats: If Janice plans to apply multiple coats of paint, she should account for the extra paint needed.By considering these factors and making an accurate estimate, Janice can ensure that she buys the right amount of paint for her new apartment.
What’s 18/100 in simplest form
Answer:
9/50
Step-by-step explanation:
18/100
Divide the top and bottom by 2
9/50
This is in simplest form
The results of a survey of common allergies was organized into a Venn diagram. Answer the questions about the following sets: D = {x | x is a person allergic to dogs}; C = {x | x is a person allergic to cats}; P = {x | x is a person allergic to pollen} How many people are not allergic to any of the three choices? How many people are allergic to all three choices? How many people are allergic to both dogs and cats but not allergic to pollen? How many people are allergic to cats only?
Answer:
How many people are not allergic to any of the three choices? 22
How many people are allergic to all three choices? 1
How many people are allergic to both dogs and cats but not allergic to pollen? 7
How many people are allergic to cats only? 18
A survey of common allergies
The survey of the common allergies was made to see the percentage of people affected by the same sort of allergies and analysis the disease. The Venn diagrams are thus made in order to refer to the types of diseases that elate and people can be identified.
As per the answer, the Venn people allergic to cats are 18, not allergic are 22, and allergic to all three is one.
The Venn diagram is one that is used to depict the relationships between the two or more finite groups of things. The diagram of the people affected by dogs, cats, and pollen is shown.The number of people who are not allergic to any of the three choices is 22. The people who are allergic to all 3 are one. The number of people allergic to both, but not to pollen is 7. Those people who are allergic to cats are 18.Hence the Venn diagram shows us the relationships.Learn more about the survey of common.
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what is the equation of the graph that represents f(x)=x^4 stretched vertically by 2 and shifted up 3 spaces
Answer: [tex]g(x)=2x^4+3[/tex]
Step-by-step explanation:
These are some transformations for a function f(x):
If [tex]f(x)+k[/tex], then the function is shifted up "k" units.
If [tex]mf(x)[/tex], and [tex]k>1[/tex], then the function is stretched vertically by a factor of "m".
Knowing this transformation and knowing that the function [tex]f(x)=x^4[/tex] is stretched vertically by 2 and shifted up 3 spaces, then we can conclude that new function, which we can call g(x), is:
[tex]g(x)=2(x^4)+3[/tex]
[tex]g(x)=2x^4+3[/tex]
What is the distance between points D and H?
round to the nearest 10th of a unit.
3.7 units
5.2 units
7.3 units
9.4 units
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ D(\stackrel{x_1}{9}~,~\stackrel{y_1}{8})\qquad H(\stackrel{x_2}{1}~,~\stackrel{y_2}{3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ DH=\sqrt{(1-9)^2+(3-8)^2}\implies DH=\sqrt{(-8)^2+(-5)^2} \\\\\\ DH=\sqrt{64+25}\implies DH=\sqrt{89}\implies DH\approx 9.4[/tex]
Convert the Cartesian equation (x 2 + y 2)2 = 4(x 2 - y 2) to a polar equation.
Choices:
r4 = -4r2
r2 = 4cos2θ
r2 = 4sin2θ
ANSWER
[tex]{r}^{2} = 4 \cos2\theta[/tex]
EXPLANATION
The Cartesian equation is
[tex] {( {x}^{2} + {y}^{2} )}^{2} = 4( {x}^{2} - {y}^{2} )[/tex]
We substitute
[tex]x = r \cos( \theta) [/tex]
[tex]y = r \sin( \theta) [/tex]
and
[tex] {x}^{2} + {y}^{2} = {r}^{2} [/tex]
This implies that
[tex] {( {r}^{2} )}^{2} = 4(( { r \cos\theta) }^{2} - {(r \sin\theta) }^{2} )[/tex]
Let us evaluate the exponents to get:
[tex] {r}^{4} = 4({ {r}^{2} \cos^{2}\theta } - {r}^{2} \sin^{2}\theta)[/tex]
Factor the RHS to get:
[tex] {r}^{4} = 4{r}^{2} ({ \cos^{2}\theta } - \sin^{2}\theta)[/tex]
Divide through by r²
[tex]{r}^{2} = 4 ({ \cos^{2}\theta } - \sin^{2}\theta)[/tex]
Apply the double angle identity
[tex]\cos^{2}\theta -\sin^{2}\theta= \cos(2 \theta) [/tex]
The polar equation then becomes:
[tex]{r}^{2} = 4 \cos2\theta[/tex]
To convert the Cartesian equation to polar form, we substitute x and y with polar coordinates r and theta. Simplifying the equation with trigonometric identities leads to a polar equation, r^2 = 4cos^2\theta, which is the correct option among those given.
Explanation:To convert the Cartesian equation (x^2 + y^2)^2 = 4(x^2 - y^2) to a polar equation, we use the relationships x = r\cos\theta and y = r\sin\theta. Substituting these into the given equation, we get:
(r^2\cos^2\theta + r^2\sin^2\theta)^2 = 4(r^2\cos^2\theta - r^2\sin^2\theta)
This simplifies to:
r^4 = 4r^2(\cos^2\theta - \sin^2\theta)
Using the double angle identity for cosine, \cos(2\theta) = \cos^2\theta - \sin^2\theta, we can further simplify:
r^4 = 4r^2\cos(2\theta)
Dividing both sides by r^2, as long as r \neq 0, gives us:
r^2 = 4\cos(2\theta)
However, this is not one of the provided options, so we must go further and use another trigonometric identity:
\cos(2\theta) = 2\cos^2\theta - 1
The equation r^2 = 4\cos(2\theta) can then be rewritten as:
r^2 = 4(2\cos^2\theta - 1)
Since this is still not aligning with the provided options, it is important to check the original approach. There may have been a simplification error or a misinterpretation of the trigonometric identities. The correct polar equation that corresponds to the given choices should indeed be r^2 = 4\cos^2\theta, which is found by recognizing that \cos(2\theta) can also be written as 2\cos^2\theta - 1.
what are the solutions to the equation x - (7/x) = 6
Answer: c. x=-1 and x=7
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
arrange the expressions in ascending order of their values when x=-2
1-x^2over1-2x
x2-1over1-2x
2x^2+xover2
3x^2+1over2(x-1)
Answer:
The expressions in ascending order would be:
[tex]\frac{3x^2+1}{2(x-1)} < \frac{x^2-1}{1-2x} < \frac{x^2}{1-2x} < \frac{2x^2+x}{2}[/tex]
At x = -2
Explanation:
First, we will evaluate the given expressions at x = -2
1- The first expression:
[tex]\frac{x^2}{1-2x}=\frac{(-2)^2}{1-2(-2)}=\frac{4}{5}[/tex]
2- The second expression:
[tex]\frac{x^2-1}{1-2x}=\frac{(-2)^2-1}{1-2(-2)}=\frac{3}{5}[/tex]
3- The third expression:
[tex]\frac{2x^2+x}{2}=\frac{2(-2)^2+(-2)}{2}=3[/tex]
4- The fourth expression:
[tex]\frac{3x^2+1}{2(x-1)}=\frac{3(-2)^2+1}{2(-2-1)}=-\frac{13}{6}[/tex]
Then, we will arrange the values in an ascending order:
[tex]-\frac{13}{6} < \frac{3}{5} < \frac{4}{5} < 3[/tex]
Finally, we arrange the expressions based on the value arrangement:
[tex]\frac{3x^2+1}{2(x-1)} < \frac{x^2-1}{1-2x} < \frac{x^2}{1-2x} < \frac{2x^2+x}{2}[/tex]
Hope this helps :)
Please please please help me!!!!!!
Answer:
Step-by-step explanation:
Use Pythagorean theorem.
c^2 = a^2+b^2
c^2 = 4^2+6^2
c^2 = 16+36
c^2 = 52
c = √52 = 7.21
Which of the following equations are equivalent to -2m - 5m - 8 = 3 + (-7) + m?
-15m = -4m
-7m - 8 = m - 4
-3m - 8 = 4 - m
m - 4 = -7m - 8
-8 - 7m = -4 + m
-8 - 3m = 4 - m
Answer:
B) -7m - 8 = m - 4
D) m - 4 = -7m - 8
E) -8 - 7m = -4 + m
Step-by-step explanation:
Solve all of the equations to see if they end up with the same result. Start with the original:
-2m - 5m - 8 = 3 + (-7) + m
-7m - 8 = -4 + m (now we know B and D and E are correct)
-7m - m - 8 = -4 + m - m
-8m - 8 = -4
-8m - 8 + 8= -4 + 8
-8m = 4
Answer:
-7m - 8 = m - 4
m - 4 = -7m - 8
-8 - 7m = -4 + m
Step-by-step explanation:
Given equation,
-2m - 5m - 8 = 3 + (-7) + m,
Combining like terms,
-7m - 8 =-4 + m
Subtract m from both sides,
-8m - 8 = -4
Add 8 on both sides,
-8m = 4
Divide both sides by -8,
m = [tex]-\frac{1}{2}[/tex]
(i) -15m = -4m ⇒ -15m + 4m = 0 ⇒ -11m = 0 ⇒ m = 0
(ii) -7m - 8 = m - 4 ⇒ -7m - m = -4 + 8 ⇒ -8m = 4 ⇒ m = [tex]-\frac{1}{2}[/tex]
(iii) -3m - 8 = 4 - m ⇒ -3m + m = 4 + 8 ⇒ -2m = 12 ⇒ m = -6
(iv) m - 4 = -7m - 8 ⇒ m + 7m = -8 + 4 ⇒ 8m = -4 ⇒ m = [tex]-\frac{1}{2}[/tex]
(v) -8 - 7m = -4 + m ⇒ -7m - m = -4 + 8 ⇒ -8m = 4 ⇒ m = [tex]-\frac{1}{2}[/tex]
(vi) -8 - 3m = 4 - m ⇒ -3m + m = 4 + 8 ⇒ -2m = 12 ⇒ m = -6
this sign tells drivers there is a steep hill ahead. write the number of sides and the number of angles in the shape of this sign
The yellow diamond-shaped traffic sign in the image has 4 sides and 4 angles. It’s a common warning sign used worldwide to alert drivers of a steep downhill grade ahead. The downward-pointing chevron symbol within the diamond further emphasizes the descending slope.
Here’s a quick breakdown of its geometrical features:
Shape: Diamond (also known as a rhombus)
Sides: 4, all of equal length
Angles: 4, with two acute angles (less than 90°) and two obtuse angles (more than 90°)
Properties: Opposite sides are parallel, diagonals bisect each other at right angles.
The diamond shape in traffic signs often conveys caution or warning, especially when paired with specific symbols like the downward chevron.
What is the integration of cos3x
Answer:
1/3 sin(3x)+C
Step-by-step explanation:
int (cos(3x) dx)
Let u=3x then du=3 dx so 1/3 du=dx
rewriting integral
int(1/3 cos(u) du)
now evaluating
1/3 sin(u)+C since (sin(u))'=cos(u)
Replace u with 3x
Answer is 1/3 sin(3x)+C
Answer:
Step-by-step explanation:
Integral of cos3x = ⅓sin3x
So when integrating just simply multiply by reciprocal of the cooeffecient of the angle and the integral of that particular trig ratio, in this case it's the sinx.
Larry wants to buy some carpeting for his living room. the length of the room is 4 times the width and the total area of the room is 16 square meters. What is the length of the living room
Answer:
I would say the length is 8 and the width is 2
Step-by-step explanation:
Note that : ( Length = L , Width = W , Area = A)
A = L x W - the area is 16 as given in the question, therefore:
16 = L x W <- this is your 1st equation
L = 4W - Length is 4 times the width, this is your second equation
Take your second equation and substitute it into the first one:
16 = 4W x W -> simplify this:
16 = 4W^2
Divide both sides of the equation by 4 to isolate the W^2
16 ÷ 4 = (4w^2) ÷ 4 -> this will equal to:
4 = w^2
Now you want to get rid of '^2', you want to isolate w. To do this you need to find the square root of both sides of the equation
√ 4 = √ w^2 -> this will equal to:
2 = w
Now that you have the value of w just sub it into the first equation
16 = L x W
16 = L x 2
16 ÷ 2 = L
8 = L
therefore the length is 8 and the width is 2
What is the slope of the line passing through the points (1,57) and (2,27)?
Answer:
-30.
Step-by-step explanation:
Slope = rise / run
= (57-27) / (1 - 2)
= -30.
The slope of the line passing through points (1,57) and (2,27) is; 30.
What is the slope?The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.
It can be calculated as;
Slope = rise/run
Given that the line passes through points (1,57) and (2,27), we need to find the slope of the line.
Slope = rise/run
Slope = (57-27) / (1 - 2)
Slope = -30.
Therefore, the slope of the line passing through points (1,57) and (2,27) is; 30.
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what is the value of x, given that the two prisms are similar?
Answer:
The correct answer option is D. 60.
Step-by-step explanation:
We are given the diagram of two prisms with known side lengths other than x. Given that these prisms are similar, we are to find the value of x.
Considering the similarity of these prisms, we will use the ratio method to find x.
[tex] \frac { 3 } { 2 0 } = \frac { 9 } { x } [/tex]
[tex] x = \frac { 6 \times 2 0 } { 3 } [/tex]
x = 60
Answer: OPTION D
Step-by-step explanation:
Given the similar prisms shown in the image, the first step is to set up the following proportion, where "x" is the missing lenght:
[tex]\frac{9}{3}=\frac{x}{20}[/tex]
And finally you need to solve for the lenght "x" to find its value.
To solve for "x" you can multiply both sides of the equation by 20.
Then, the result is:
[tex](20)(\frac{9}{3})=(\frac{x}{20})(20)\\\\\frac{9*20}{3}=x\\\\\frac{180}{3}=x\\\\x=60[/tex]
-2xy-x+4y para y=-3 x=9
Answer: 33
if you add them all up,they are 33
What is the slop of the line containing the points (4,-10 2/3), (-3,1)
let's firstly convert the mixed fraction to improper fraction.
[tex]\bf \stackrel{mixed}{10\frac{2}{3}}\implies \cfrac{10\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{32}{3}} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{4}~,~\stackrel{y_1}{-\frac{32}{3}})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-\left( -\frac{32}{3} \right)}{-3-4}\implies \cfrac{1+\frac{32}{3}}{-7}\implies \cfrac{\frac{3+32}{3}}{-7}[/tex]
[tex]\bf \cfrac{~~\frac{35}{3}~~}{\frac{-7}{1}} \implies \cfrac{\stackrel{5}{~~\begin{matrix} 35 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}~~}{3}\cdot \cfrac{1}{~~\begin{matrix} -7 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies -\cfrac{5}{3}[/tex]
Ceilia uses the steps below to solve the equation -3/8 (-8-16d) + 2d= 24
Step 1. Distribute -3/8 over the expression in parentheses
Step 2.Simplify like terms
Step 3. Subtract 3 from both sides
Step 4. Divide both sides by the equation by -14
Which step had an error?
The incorrect step and with error is subtract 3 from both sides. Option 3
We have that the equation is;
-3/8 (-8-16d) + 2d= 24
multiply the values, we get;
-24 + 48d + 2d = 24
add the like terms
-24 + 50d = 24
50d = 48
d = 48/50
The other steps are;
Subtract 3 from both sides (However, the instruction mentions subtracting 3, but there is no number 3 in the equation.
Divide both sides by the equation by -14
Evaluate 12 X (1.4+8.59) writing your answer in its simplest form.
Step-by-step explanation:
1.4+8.59= 9.99
12 X 9.99 = 119.88
What is the mode for the set of values?
307 309 323 304 390 398
@ 316
6 339
© 345
(d) no
mode
Answer:
D no mode
Step-by-step explanation:
You need to have a number seen at least twice to have a mode.
Answer:
There is no mode
Step-by-step explanation:
Mode is when numbers are repeated, and there are no numbers repeated
Write the expression in complete factored form.
x(y-2) + 5(y-2) =
Answer:
(y-2) (x+5)
Step-by-step explanation:
x(y-2) + 5(y-2) =
We can factor out the expression (y-2), leaving us with x+5
(y-2) (x+5)
Answer: (x+5)(y-2)
Because the x and the 5 are being multiplied by the same factor you can change it to make the answer (x+5)(y-2)
-3x + 1 + 10x = x + 4
x = 1/2
x = 5/6
x = 12
x = 18
Answer:
A
Step-by-step explanation:
Given
- 3x + 1 + 10x = x + 4 ( simplify left side )
7x + 1 = x + 4 ( subtract x from both sides )
6x + 1 = 4 ( subtract 1 from both sides )
6x = 3 ( divide both sides by 6 )
x = [tex]\frac{3}{6}[/tex] = [tex]\frac{1}{2}[/tex]
4⁄15 of the 315 members of a book club are male. How many female members are there in the club?
What is the solution to the system of equations graphed below?
Answer:
B
Step-by-step explanation:
The solution to a system of equations given graphically is at the point of intersection of the 2 lines, that is
solution = (0, - 4) → B
Answer:
B (0,-4)
Step-by-step explanation:
The solution to a system of equations is where the graphs intersect.
The two lines cross at x=0, y= -4
The radius of a circle is 2 centimeters. What is the circle's area?
Answer:
I just know its formula 2 pie r square
Step-by-step explanation:
Answer: A = 12.56 cm
Step-by-step explanation:
A = 3.14 x r^2
A = 3.14 x 2^2
A = 3.14 x 4
A = 12.56 cm
Length of shawdow of building 32m. The distance from the top to the tip of the shadow is 38m . find the height of the building
Answer:
20.49 feet to the nearest hundredth.
Step-by-step explanation:
Using the Pythagoras Theorem:
38^2 = h^2 + 32^2
h^2 = 38^2 - 32^2
h^2 = 420
h = √420
h = 20.494 m.
Your question asks to find the height of the building.
Answer: 20.49 metersTo find the answer to your question, we would need to use the Pythagorean theorem.
Pythagorean Theorem: [tex]a^2+b^2=c^2[/tex]
What we would do is plug in the numbers that we already know into the equation, and then we simply solve.
We would plug 32 to a and plug 38 into c
Your equation should look like this:
[tex]32^2+b^2=38^2[/tex]
Now, we solve:
[tex]32^2+b^2=38^2\\\\1024+b^2=38^2\\\\1024+b^2=1444\\\\b^2=420\\\\\sqrt{b} =\sqrt{420} \\\\b=20.493[/tex]
We would jkust round to the nearest hundredths place, therefore giving you the answer of 20.49.
This means that the height of the building would be 20.49 meters
20.49 meters would be your FINAL answer.
I hope this helps!Best regards, MasterInvestorIndicate the method you would use to prove the two A's 2. If no method applies, enter none.
Answer:
HL
Step-by-step explanation:
You have a the two hypotenuses from the two triangles are congruent.
You also have a pair of of legs from each of the triangles that are congruent.
So HL means hypotenuse-leg which is what you have in the pic!
Final answer:
To prove two 'A's are equivalent, methods such as direct proof, disjunctive syllogism, conditional proof, and indirect proof can be applied. The selection of the method depends on the nature of the proof and the preference of the solver.
Explanation:
To establish that both 'A's are equivalent in a given proof, one might utilize several methods including direct proof, disjunctive syllogism, conditional proof, or indirect proof. For instance, a disjunctive syllogism can be employed when an argument has an either/or scenario, which allows for a conclusion to be drawn when one of the options is eliminated. Conversely, if you aim to reach a conclusion in the form of a conditional A → B, you might opt for a conditional proof method where you start a subproof by assuming A and then proceed to derive B within that subproof. In cases where a direct proof is challenging, you might resort to an indirect proof approach by assuming the negation of what you're attempting to prove and then showing this leads to a contradiction.
Direct proof and indirect proof are both formally legitimate, even though one might offer a more straightforward path to the solution or resonate more with the problem-solver's reasoning style. When planning an experiment or mapping out a mathematical proof, it is vital to consider the different methods and choose one that aligns with the nature of the problem and the proof you wish to establish.
An Internet and cable-television supplier surveyed a random sample of their customers. The results are shown in the table.
Which statement about the two-way frequency table is true?
A.
The survey represents quantitative data.
B.
There is a greater percentage of Internet customers who are not satisfied than cable television customers who are not
satisfied.
C.
About half of the customers surveyed are cable-television customers.
D.
About one-fourth of the cable-television customers are not satisfied.
Answer:
D) About one-fourth of the cable-television customers are not satisfied.
Step-by-step explanation:
First you find out how many cable-television customers are not satisfied, which is 285. The you find out the total number of cable-television users in the sample, which is 1,109. Then you divide the number of unsatisfied by the total, 285/1109, to get .2569 or 25%
Answer:D) About one-fourth of the cable-television customers are not satisfied.
Step-by-step explanation:
What is the lateral area of a prism which has a lateral edge of 4 inches and has a regular pentagonal base with an edge of 12 inches?
Check the picture below.
so the pentagonal prism in the picture is been seen from the bottom, namely so we can see its base, however the base is at the bottom, what does that mean, it means that the pentagonal bases are the top and bottom of the prism, that matters, because the other sides are the lateral sides.
so, if we notice, the lateral sides are really just 5 rectangles, each one a 12x4, so if we simply get the area of all those rectangles.
5(12 * 4) = 240 in².
The lateral area of the given regular pentagonal prism is 240 square inches, calculated using the formula Lateral Area = Perimeter of Base * Lateral Edge.
Explanation:The lateral area of a prism, particularly a regular pentagonal prism, can be calculated using the formula Lateral Area = Perimeter of Base * Lateral Edge. In this case, the base is a regular pentagon implying that all its sides are equal. Therefore, its perimeter would be 60 inches (12 inches * 5 sides).
The lateral edge is given as 4 inches. Applying the values to the formula, we get Lateral Area = 60 inches * 4 inches = 240 square inches.
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Which equation has only one solution?
Ox-51 = -1
1-6 - 2x1 = 8
15x + 10 = 10
O |-6x +31 = 0
Answer:
I would say the third one ( 15x + 10 = 10 )
Step-by-step explanation:
I say this because, if we take 10 from both sides, 15x = 0. Even if you tried to divide by 15, x = 0. x also =0 if you try to do it the other way by finding what times 15 +10 = 10 it would be zero. The third one is your Answerr
Since the only solution to the equation is 0, hence 15x + 10 = 10 is the only equation With a solution.
Equation of functions With only one solution
Equations With just one solution are knoWn to have a leading degree of one and Without a modulus sign
Fro the linear function 15x + 10 = 10
Check:
Subtract 10 from both sides
15x + 10 - 10 = 10 - 10
15x = 10 - 10
15x = 0
Dividde both sides by 15 to have:
15x/15 = 0/15
x = 0
Since the only solution to the equation is 0, hence 15x + 10 = 10 is the only equation With a solution.
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Factor 15x^3 - 5x^2 +6x-2 by grouping. what is the resulting expression
Answer:
(3x - 1)(5x^2 + 2)
Step-by-step explanation:
15x^3 - 5x^2 (the first two terms) have the common factor 5x^2, so that
15x^3 - 5x^2 = (5x^2)(3x - 1).
Likewise, 6x - 2 = 2(3x - 1).
Thus, 15x^3 - 5x^2 +6x-2 can be written as (3x - 1)(5x^2 + 2)