SOLUTION: Factor completely: 8p^2 + 7pq - 18q^2 Can someone please explain to me in detail how to answer this question..

Question 318368: Factor completely:
8p^2 + 7pq - 18q^2
Can someone please explain to me in detail how to answer this question..
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Looking at we can see that the first term is and the last term is where the coefficients are 8 and -18 respectively.

Now multiply the first coefficient 8 and the last coefficient -18 to get -144. Now what two numbers multiply to -144 and add to the middle coefficient 7? Let's list all of the factors of -144:

Factors of -144:
1,2,3,4,6,8,9,12,16,18,24,36,48,72

-1,-2,-3,-4,-6,-8,-9,-12,-16,-18,-24,-36,-48,-72 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -144
(1)*(-144)
(2)*(-72)
(3)*(-48)
(4)*(-36)
(6)*(-24)
(8)*(-18)
(9)*(-16)
(-1)*(144)
(-2)*(72)
(-3)*(48)
(-4)*(36)
(-6)*(24)
(-8)*(18)
(-9)*(16)

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

Now which of these pairs add to 7? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 7

First Number	Second Number	Sum
1	-144	1+(-144)=-143
2	-72	2+(-72)=-70
3	-48	3+(-48)=-45
4	-36	4+(-36)=-32
6	-24	6+(-24)=-18
8	-18	8+(-18)=-10
9	-16	9+(-16)=-7
-1	144	-1+144=143
-2	72	-2+72=70
-3	48	-3+48=45
-4	36	-4+36=32
-6	24	-6+24=18
-8	18	-8+18=10
-9	16	-9+16=7

From this list we can see that -9 and 16 add up to 7 and multiply to -144

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 )

------------------------------------------------------------

Answer:
So factors to

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