SOLUTION: please factor out polynomial. 8x^3-14x^2-15x thanks

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Question 187131: please factor out polynomial.

8x^3-14x^2-15x

thanks
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

8x%5E3-14x%5E2-15x Start with the given expression


x%288x%5E2-14x-15%29 Factor out the GCF x


Now let's focus on the inner expression 8x%5E2-14x-15




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Looking at 8x%5E2-14x-15 we can see that the first term is 8x%5E2 and the last term is -15 where the coefficients are 8 and -15 respectively.

Now multiply the first coefficient 8 and the last coefficient -15 to get -120. Now what two numbers multiply to -120 and add to the middle coefficient -14? Let's list all of the factors of -120:



Factors of -120:
1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120

-1,-2,-3,-4,-5,-6,-8,-10,-12,-15,-20,-24,-30,-40,-60,-120 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -120
(1)*(-120)
(2)*(-60)
(3)*(-40)
(4)*(-30)
(5)*(-24)
(6)*(-20)
(8)*(-15)
(10)*(-12)
(-1)*(120)
(-2)*(60)
(-3)*(40)
(-4)*(30)
(-5)*(24)
(-6)*(20)
(-8)*(15)
(-10)*(12)

note: remember, the product of a negative and a positive number is a negative number


Now which of these pairs add to -14? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -14

First NumberSecond NumberSum
1-1201+(-120)=-119
2-602+(-60)=-58
3-403+(-40)=-37
4-304+(-30)=-26
5-245+(-24)=-19
6-206+(-20)=-14
8-158+(-15)=-7
10-1210+(-12)=-2
-1120-1+120=119
-260-2+60=58
-340-3+40=37
-430-4+30=26
-524-5+24=19
-620-6+20=14
-815-8+15=7
-1012-10+12=2



From this list we can see that 6 and -20 add up to -14 and multiply to -120


Now looking at the expression 8x%5E2-14x-15, replace -14x with 6x%2B-20x (notice 6x%2B-20x adds up to -14x. So it is equivalent to -14x)

8x%5E2%2Bhighlight%286x%2B-20x%29%2B-15


Now let's factor 8x%5E2%2B6x-20x-15 by grouping:


%288x%5E2%2B6x%29%2B%28-20x-15%29 Group like terms


2x%284x%2B3%29-5%284x%2B3%29 Factor out the GCF of 2x out of the first group. Factor out the GCF of -5 out of the second group


%282x-5%29%284x%2B3%29 Since we have a common term of 4x%2B3, we can combine like terms

So 8x%5E2%2B6x-20x-15 factors to %282x-5%29%284x%2B3%29


So this also means that 8x%5E2-14x-15 factors to %282x-5%29%284x%2B3%29 (since 8x%5E2-14x-15 is equivalent to 8x%5E2%2B6x-20x-15)



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So our expression goes from x%288x%5E2-14x-15%29 and factors further to x%282x-5%29%284x%2B3%29


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Answer:

So 8x%5E3-14x%5E2-15x factors to x%282x-5%29%284x%2B3%29