SOLUTION: graph: y= -3x^2+2 Thank You!

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Question 718706: graph: y= -3x^2+2 Thank You!
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!

Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)


Start with the given expression.



Factor out the GCF .



Now let's try to factor the inner expression



---------------------------------------------------------------



Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is .



Now multiply the first coefficient by the last term to get .



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



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



Factors of :

1,2,3,6

-1,-2,-3,-6



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



These factors pair up and multiply to .

1*(-6) = -6
2*(-3) = -6
(-1)*(6) = -6
(-2)*(3) = -6


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



First NumberSecond NumberSum
1-61+(-6)=-5
2-32+(-3)=-1
-16-1+6=5
-23-2+3=1




From the table, we can see that there are no pairs of numbers which add to . So cannot be factored.



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Answer:



So simply factors to



In other words, .
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