# SOLUTION: how do you simplify 15x^2+75x-1260

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Question 347687: how do you simplify 15x^2+75x-1260

Found 2 solutions by jim_thompson5910, Fombitz:
You can put this solution on YOUR website!

Factor out the GCF

Now let's focus on the inner expression

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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 -84 respectively.

Now multiply the first coefficient 1 and the last coefficient -84 to get -84. Now what two numbers multiply to -84 and add to the middle coefficient 5? Let's list all of the factors of -84:

Factors of -84:
1,2,3,4,6,7,12,14,21,28,42,84

-1,-2,-3,-4,-6,-7,-12,-14,-21,-28,-42,-84 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -84
(1)*(-84)
(2)*(-42)
(3)*(-28)
(4)*(-21)
(6)*(-14)
(7)*(-12)
(-1)*(84)
(-2)*(42)
(-3)*(28)
(-4)*(21)
(-6)*(14)
(-7)*(12)

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

Now which of these pairs add to 5? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 5

First NumberSecond NumberSum
1-841+(-84)=-83
2-422+(-42)=-40
3-283+(-28)=-25
4-214+(-21)=-17
6-146+(-14)=-8
7-127+(-12)=-5
-184-1+84=83
-242-2+42=40
-328-3+28=25
-421-4+21=17
-614-6+14=8
-712-7+12=5

From this list we can see that -7 and 12 add up to 5 and multiply to -84

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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So our expression goes from and factors further to

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