SOLUTION: 9x^2+18x+8

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Question 117621:
9x^2+18x+8
Found 2 solutions by jim_thompson5910, checkley71:
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 9 and 8 respectively.

Now multiply the first coefficient 9 and the last coefficient 8 to get 72. Now what two numbers multiply to 72 and add to the middle coefficient 18? Let's list all of the factors of 72:



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

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

These factors pair up and multiply to 72
1*72
2*36
3*24
4*18
6*12
8*9
(-1)*(-72)
(-2)*(-36)
(-3)*(-24)
(-4)*(-18)
(-6)*(-12)
(-8)*(-9)

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


Now which of these pairs add to 18? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 18

First NumberSecond NumberSum
1721+72=73
2362+36=38
3243+24=27
4184+18=22
6126+12=18
898+9=17
-1-72-1+(-72)=-73
-2-36-2+(-36)=-38
-3-24-3+(-24)=-27
-4-18-4+(-18)=-22
-6-12-6+(-12)=-18
-8-9-8+(-9)=-17



From this list we can see that 6 and 12 add up to 18 and multiply to 72


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

Answer by checkley71(8403)   (Show Source): You can put this solution on YOUR website!
9X^2+18X+8
(3X+2)(3X+4)
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