SOLUTION: i need help with this factoring problem {{{ 7y^2+7y-18 }}} and also this one with the negative first kinda threw me off. {{{-5ab^2+10a^2b-15ab }}}

Question 168402: i need help with this factoring problem
and also this one with the negative first kinda threw me off.

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
# 1

Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is .

Now multiply the first coefficient by the last term to get .

Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ?

To find these two numbers, we need to list all of the factors of (the previous product).

Factors of :
1,2,3,6,7,9,14,18,21,42,63,126
-1,-2,-3,-6,-7,-9,-14,-18,-21,-42,-63,-126

Note: list the negative of each factor. This will allow us to find all possible combinations.

These factors pair up and multiply to .
1*(-126)
2*(-63)
3*(-42)
6*(-21)
7*(-18)
9*(-14)
(-1)*(126)
(-2)*(63)
(-3)*(42)
(-6)*(21)
(-7)*(18)
(-9)*(14)

Now let's add up each pair of factors to see if one pair adds to the middle coefficient :

First Number	Second Number	Sum
1	-126	1+(-126)=-125
2	-63	2+(-63)=-61
3	-42	3+(-42)=-39
6	-21	6+(-21)=-15
7	-18	7+(-18)=-11
9	-14	9+(-14)=-5
-1	126	-1+126=125
-2	63	-2+63=61
-3	42	-3+42=39
-6	21	-6+21=15
-7	18	-7+18=11
-9	14	-9+14=5

From the table, we can see that there are NO pairs of numbers which add to .

So CANNOT be factored.

Start with the given expression

Factor out the GCF

Since the inner term contains no other common terms or exponents, this is as far as we go.

So factors to
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