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

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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)

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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
So the original quadratic



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.
Answer:
So the quadratic factors to




Notice how foils back to our original problem . This verifies our answer.