SOLUTION: 36x4-8x3-28x2=

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Question 145714: 36x4-8x3-28x2=
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming you want to factor right?




36x%5E4-8x%5E3-28x%5E2 Start with the given expression


4x%5E2%289x%5E2-2x-7%29 Factor out the GCF 4x%5E2


Now let's focus on the inner expression 9x%5E2-2x-7




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Looking at 9x%5E2-2x-7 we can see that the first term is 9x%5E2 and the last term is -7 where the coefficients are 9 and -7 respectively.

Now multiply the first coefficient 9 and the last coefficient -7 to get -63. Now what two numbers multiply to -63 and add to the middle coefficient -2? Let's list all of the factors of -63:



Factors of -63:
1,3,7,9,21,63

-1,-3,-7,-9,-21,-63 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -63
(1)*(-63)
(3)*(-21)
(7)*(-9)
(-1)*(63)
(-3)*(21)
(-7)*(9)

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


Now which of these pairs add to -2? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -2

First NumberSecond NumberSum
1-631+(-63)=-62
3-213+(-21)=-18
7-97+(-9)=-2
-163-1+63=62
-321-3+21=18
-79-7+9=2



From this list we can see that 7 and -9 add up to -2 and multiply to -63


Now looking at the expression 9x%5E2-2x-7, replace -2x with 7x%2B-9x (notice 7x%2B-9x adds up to -2x. So it is equivalent to -2x)

9x%5E2%2Bhighlight%287x%2B-9x%29%2B-7


Now let's factor 9x%5E2%2B7x-9x-7 by grouping:


%289x%5E2%2B7x%29%2B%28-9x-7%29 Group like terms


x%289x%2B7%29-1%289x%2B7%29 Factor out the GCF of x out of the first group. Factor out the GCF of -1 out of the second group


%28x-1%29%289x%2B7%29 Since we have a common term of 9x%2B7, we can combine like terms

So 9x%5E2%2B7x-9x-7 factors to %28x-1%29%289x%2B7%29


So this also means that 9x%5E2-2x-7 factors to %28x-1%29%289x%2B7%29 (since 9x%5E2-2x-7 is equivalent to 9x%5E2%2B7x-9x-7)



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So our expression goes from 4x%5E2%289x%5E2-2x-7%29 and factors further to 4x%5E2%28x-1%29%289x%2B7%29


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Answer:

So 36x%5E4-8x%5E3-28x%5E2 factors to 4x%5E2%28x-1%29%289x%2B7%29