# SOLUTION: Factor completely and match your result to the correct answer below. r2 + 2r – 80 A)(r + 10)(r + 8) B)(r – 10)(r + 8) C)(r – 10)(r – 8) D)(r + 10)(r – 8)

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Question 140011: Factor completely and match your result to the correct answer below.
r2 + 2r – 80
A)(r + 10)(r + 8)
B)(r – 10)(r + 8)
C)(r – 10)(r – 8)
D)(r + 10)(r – 8)

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Looking at we can see that the first term is and the last term is where the coefficients are 1 and -80 respectively.

Now multiply the first coefficient 1 and the last coefficient -80 to get -80. Now what two numbers multiply to -80 and add to the middle coefficient 2? Let's list all of the factors of -80:

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

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

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

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
1-801+(-80)=-79
2-402+(-40)=-38
4-204+(-20)=-16
5-165+(-16)=-11
8-108+(-10)=-2
-180-1+80=79
-240-2+40=38
-420-4+20=16
-516-5+16=11
-810-8+10=2

From this list we can see that -8 and 10 add up to 2 and multiply to -80

Now looking at the expression , replace with (notice adds up to . So it is equivalent to )

Now let's factor by grouping:

Group like terms

Factor out the GCF of out of the first group. Factor out the GCF of out of the second group

Since we have a common term of , we can combine like terms

So factors to

So this also means that factors to (since is equivalent to )

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