# SOLUTION: 3x^2 + 8x + 5 how would i factor this ?

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Question 115652: 3x^2 + 8x + 5 how would i factor this ?
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Looking at we can see that the first term is and the last term is where the coefficients are 3 and 5 respectively.

Now multiply the first coefficient 3 and the last coefficient 5 to get 15. Now what two numbers multiply to 15 and add to the middle coefficient 8? Let's list all of the factors of 15:

Factors of 15:
1,3,5,15

-1,-3,-5,-15 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to 15
1*15
3*5
(-1)*(-15)
(-3)*(-5)

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

Now which of these pairs add to 8? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 8

First NumberSecond NumberSum
1151+15=16
353+5=8
-1-15-1+(-15)=-16
-3-5-3+(-5)=-8

From this list we can see that 3 and 5 add up to 8 and multiply to 15

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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