SOLUTION: 5y^2-28y-12

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Question 183247: 5y^2-28y-12
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming that you want to factor this.



Looking at the expression 5y%5E2-28y-12, we can see that the first coefficient is 5, the second coefficient is -28, and the last term is -12.


Now multiply the first coefficient 5 by the last term -12 to get %285%29%28-12%29=-60.


Now the question is: what two whole numbers multiply to -60 (the previous product) and add to the second coefficient -28?


To find these two numbers, we need to list all of the factors of -60 (the previous product).


Factors of -60:
1,2,3,4,5,6,10,12,15,20,30,60
-1,-2,-3,-4,-5,-6,-10,-12,-15,-20,-30,-60


Note: list the negative of each factor. This will allow us to find all possible combinations.


These factors pair up and multiply to -60.
1*(-60)
2*(-30)
3*(-20)
4*(-15)
5*(-12)
6*(-10)
(-1)*(60)
(-2)*(30)
(-3)*(20)
(-4)*(15)
(-5)*(12)
(-6)*(10)

Now let's add up each pair of factors to see if one pair adds to the middle coefficient -28:


First NumberSecond NumberSum
1-601+(-60)=-59
2-302+(-30)=-28
3-203+(-20)=-17
4-154+(-15)=-11
5-125+(-12)=-7
6-106+(-10)=-4
-160-1+60=59
-230-2+30=28
-320-3+20=17
-415-4+15=11
-512-5+12=7
-610-6+10=4



From the table, we can see that the two numbers 2 and -30 add to -28 (the middle coefficient).


So the two numbers 2 and -30 both multiply to -60 and add to -28


Now replace the middle term -28y with 2y-30y. Remember, 2 and -30 add to -28. So this shows us that 2y-30y=-28y.


5y%5E2%2Bhighlight%282y-30y%29-12 Replace the second term -28y with 2y-30y.


%285y%5E2%2B2y%29%2B%28-30y-12%29 Group the terms into two pairs.


y%285y%2B2%29%2B%28-30y-12%29 Factor out the GCF y from the first group.


y%285y%2B2%29-6%285y%2B2%29 Factor out 6 from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.


%28y-6%29%285y%2B2%29 Combine like terms. Or factor out the common term 5y%2B2

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Answer:


So 5y%5E2-28y-12 factors to %28y-6%29%285y%2B2%29.


In other words, 5y%5E2-28y-12=%28y-6%29%285y%2B2%29.


Note: you can check the answer by FOILing %28y-6%29%285y%2B2%29 to get 5y%5E2-28y-12 or by graphing the original expression and the answer (the two graphs should be identical).