# SOLUTION: what are the steps to factoring this problem 3(x)2+8x+5

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Question 297405: what are the steps to factoring this problem 3(x)2+8x+5
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3x^2+8x+5
Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)
In order to factor , first multiply the leading coefficient 3 and the last term 5 to get 15. Now we need to ask ourselves: What two numbers multiply to 15 and add to 8? Lets find out by listing all of the possible factors of 15

Factors:

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 to multiply to 15.

1*15=15

3*5=15

(-1)*(-15)=15

(-3)*(-5)=15

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

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 First Number | Second Number | Sum 1 | 15 | 1+15=16 3 | 5 | 3+5=8 -1 | -15 | -1+(-15)=-16 -3 | -5 | -3+(-5)=-8

We can see from the table that 3 and 5 add to 8. So the two numbers that multiply to 15 and add to 8 are: 3 and 5

breaks down to this (just replace with the two numbers that multiply to 15 and add to 8, which are: 3 and 5)

Replace with

Group the first two terms together and the last two terms together like this:

Factor a 3x out of the first group and factor a 5 out of the second group.

Now since we have a common term we can combine the two terms.

Combine like terms.
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