SOLUTION: Factor completely. 2p squared + 11p + 12

Question 115002: Factor completely.
2p squared + 11p + 12
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 2 and 12 respectively.

Now multiply the first coefficient 2 and the last coefficient 12 to get 24. Now what two numbers multiply to 24 and add to the middle coefficient 11? Let's list all of the factors of 24:

Factors of 24:
1,2,3,4,6,8,12,24

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

These factors pair up and multiply to 24
1*24
2*12
3*8
4*6
(-1)*(-24)
(-2)*(-12)
(-3)*(-8)
(-4)*(-6)

note: remember two negative numbers multiplied together make a positive number

Now which of these pairs add to 11? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 11

First Number	Second Number	Sum
1	24	1+24=25
2	12	2+12=14
3	8	3+8=11
4	6	4+6=10
-1	-24	-1+(-24)=-25
-2	-12	-2+(-12)=-14
-3	-8	-3+(-8)=-11
-4	-6	-4+(-6)=-10

From this list we can see that 3 and 8 add up to 11 and multiply to 24

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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