SOLUTION: Factor completely: x^2 + 9x + 8

Question 145892: Factor completely:
x^2 + 9x + 8

Found 2 solutions by scott8148, jim_thompson5910:
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
(x+8)(x+1)
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 1 and 8 respectively.

Now multiply the first coefficient 1 and the last coefficient 8 to get 8. Now what two numbers multiply to 8 and add to the middle coefficient 9? Let's list all of the factors of 8:

Factors of 8:
1,2,4,8

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

These factors pair up and multiply to 8
1*8
2*4
(-1)*(-8)
(-2)*(-4)

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

Now which of these pairs add to 9? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 9

First Number Second Number Sum
1 8 1+8=9
2 4 2+4=6
-1 -8 -1+(-8)=-9
-2 -4 -2+(-4)=-6

From this list we can see that 1 and 8 add up to 9 and multiply to 8

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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