SOLUTION: What is the factorization of 20xsquared+27x-8

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Question 336721: What is the factorization of 20xsquared+27x-8
Found 2 solutions by Fombitz, jim_thompson5910:
Answer by Fombitz(32388) About Me  (Show Source):
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Looking at 20x%5E2%2B27x-8 we can see that the first term is 20x%5E2 and the last term is -8 where the coefficients are 20 and -8 respectively.

Now multiply the first coefficient 20 and the last coefficient -8 to get -160. Now what two numbers multiply to -160 and add to the middle coefficient 27? Let's list all of the factors of -160:



Factors of -160:
1,2,4,5,8,10,16,20,32,40,80,160

-1,-2,-4,-5,-8,-10,-16,-20,-32,-40,-80,-160 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -160
(1)*(-160)
(2)*(-80)
(4)*(-40)
(5)*(-32)
(8)*(-20)
(10)*(-16)
(-1)*(160)
(-2)*(80)
(-4)*(40)
(-5)*(32)
(-8)*(20)
(-10)*(16)

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


Now which of these pairs add to 27? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 27

First NumberSecond NumberSum
1-1601+(-160)=-159
2-802+(-80)=-78
4-404+(-40)=-36
5-325+(-32)=-27
8-208+(-20)=-12
10-1610+(-16)=-6
-1160-1+160=159
-280-2+80=78
-440-4+40=36
-532-5+32=27
-820-8+20=12
-1016-10+16=6



From this list we can see that -5 and 32 add up to 27 and multiply to -160


Now looking at the expression 20x%5E2%2B27x-8, replace 27x with -5x%2B32x (notice -5x%2B32x adds up to 27x. So it is equivalent to 27x)

20x%5E2%2Bhighlight%28-5x%2B32x%29%2B-8


Now let's factor 20x%5E2-5x%2B32x-8 by grouping:


%2820x%5E2-5x%29%2B%2832x-8%29 Group like terms


5x%284x-1%29%2B8%284x-1%29 Factor out the GCF of 5x out of the first group. Factor out the GCF of 8 out of the second group


%285x%2B8%29%284x-1%29 Since we have a common term of 4x-1, we can combine like terms

So 20x%5E2-5x%2B32x-8 factors to %285x%2B8%29%284x-1%29


So this also means that 20x%5E2%2B27x-8 factors to %285x%2B8%29%284x-1%29 (since 20x%5E2%2B27x-8 is equivalent to 20x%5E2-5x%2B32x-8)



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Answer:
So 20x%5E2%2B27x-8 factors to %285x%2B8%29%284x-1%29



If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my website.

Jim