SOLUTION: 12y^2+5y-3

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Question 385262: 12y^2+5y-3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming you want to factor this.


Looking at the expression 12y%5E2%2B5y-3, we can see that the first coefficient is 12, the second coefficient is 5, and the last term is -3.


Now multiply the first coefficient 12 by the last term -3 to get %2812%29%28-3%29=-36.


Now the question is: what two whole numbers multiply to -36 (the previous product) and add to the second coefficient 5?


To find these two numbers, we need to list all of the factors of -36 (the previous product).


Factors of -36:
1,2,3,4,6,9,12,18,36
-1,-2,-3,-4,-6,-9,-12,-18,-36


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


These factors pair up and multiply to -36.
1*(-36) = -36
2*(-18) = -36
3*(-12) = -36
4*(-9) = -36
6*(-6) = -36
(-1)*(36) = -36
(-2)*(18) = -36
(-3)*(12) = -36
(-4)*(9) = -36
(-6)*(6) = -36

Now let's add up each pair of factors to see if one pair adds to the middle coefficient 5:


First NumberSecond NumberSum
1-361+(-36)=-35
2-182+(-18)=-16
3-123+(-12)=-9
4-94+(-9)=-5
6-66+(-6)=0
-136-1+36=35
-218-2+18=16
-312-3+12=9
-49-4+9=5
-66-6+6=0



From the table, we can see that the two numbers -4 and 9 add to 5 (the middle coefficient).


So the two numbers -4 and 9 both multiply to -36 and add to 5


Now replace the middle term 5y with -4y%2B9y. Remember, -4 and 9 add to 5. So this shows us that -4y%2B9y=5y.


12y%5E2%2Bhighlight%28-4y%2B9y%29-3 Replace the second term 5y with -4y%2B9y.


%2812y%5E2-4y%29%2B%289y-3%29 Group the terms into two pairs.


4y%283y-1%29%2B%289y-3%29 Factor out the GCF 4y from the first group.


4y%283y-1%29%2B3%283y-1%29 Factor out 3 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.


%284y%2B3%29%283y-1%29 Combine like terms. Or factor out the common term 3y-1


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Answer:


So 12y%5E2%2B5y-3 factors to %284y%2B3%29%283y-1%29.


In other words, 12y%5E2%2B5y-3=%284y%2B3%29%283y-1%29.


Note: you can check the answer by expanding %284y%2B3%29%283y-1%29 to get 12y%5E2%2B5y-3 or by graphing the original expression and the answer (the two graphs should be identical).


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim