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) About Me  (Show Source):
You can put this solution on YOUR website!

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


-3%2Ax%5E2%2B0%2Ax%2B2 Start with the given expression.



-%283x%5E2%2B0x-2%29 Factor out the GCF -1.



Now let's try to factor the inner expression 3x%5E2%2B0x-2



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Looking at the expression 3x%5E2%2B0x-2, we can see that the first coefficient is 3, the second coefficient is 0, and the last term is -2.



Now multiply the first coefficient 3 by the last term -2 to get %283%29%28-2%29=-6.



Now the question is: what two whole numbers multiply to -6 (the previous product) and add to the second coefficient 0?



To find these two numbers, we need to list all of the factors of -6 (the previous product).



Factors of -6:

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 -6.

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 0:



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 0. So 3x%5E2%2B0x-2 cannot be factored.



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Answer:



So -3%2Ax%5E2%2B0%2Ax%2B2 simply factors to -%283x%5E2%2B0x-2%29



In other words, -3%2Ax%5E2%2B0%2Ax%2B2=-%283x%5E2%2B0x-2%29.