# SOLUTION: Factoring with a coefficient greater than 1 5yto the 2nd+7y-6

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Question 89355: Factoring with a coefficient greater than 1
5yto the 2nd+7y-6

Found 2 solutions by malakumar_kos@yahoo.com, jim_thompson5910:
You can put this solution on YOUR website!

Factoring with a coefficient greater than 1
5yto the 2nd+7y-6

5y^2+7y-6 = 5y^2+10y-3y-6
= 5y(y+2)-3(y+2)
= (y+2)(5y-3)

You can put this solution on YOUR website!
In order to factor , first multiply 5 and -6 to get -30 and we need to ask ourselves: What two numbers multiply to -30 and add to 7? Lets find out by listing all of the possible factors of -30

Factors:
1,2,3,5,6,10,15,30,
-1,-2,-3,-5,-6,-10,-15,-30, List the negative factors as well. This will allow us to find all possible combinations
These factors pair up to multiply to -30.
(-1)*(30)=-30
(-2)*(15)=-30
(-3)*(10)=-30
(-5)*(6)=-30
Now which of these pairs add to 7? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 7
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 First Number | Second Number | Sum 1 | -30 | 1+(-30)=-29 2 | -15 | 2+(-15)=-13 3 | -10 | 3+(-10)=-7 5 | -6 | 5+(-6)=-1 -1 | 30 | (-1)+30=29 -2 | 15 | (-2)+15=13 -3 | 10 | (-3)+10=7 -5 | 6 | (-5)+6=1
We can see from the table that -3 and 10 add to 7. So the two numbers that multiply to -30 and add to 7 are: -3 and 10

breaks down to this (just replace with the two numbers that multiply to -30 and add to 7, which are: -3 and 10)

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

Factor a y out of the first group and factor a 2 out of the second group.

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

Combine like terms.