SOLUTION: how to factor? -2x^2-3x+6

Question 708894: how to factor? -2x^2-3x+6
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

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 :
1,2,3,4,6,12
-1,-2,-3,-4,-6,-12

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

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

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

First Number	Second Number	Sum
1	-12	1+(-12)=-11
2	-6	2+(-6)=-4
3	-4	3+(-4)=-1
-1	12	-1+12=11
-2	6	-2+6=4
-3	4	-3+4=1

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

===============================================================

Answer:

So simply factors to

In other words, .

RELATED QUESTIONS
how to factor... (answered by Fombitz)

how do you factor:... (answered by richwmiller)

Factor: x^3 - 3x^2 + 2x -... (answered by ptth176)

how to factor a four term polynomial by grouping... (answered by Alan3354)

What does 2x^3-3x^2+x+6 factor out... (answered by Fombitz)

Please factor by grouping 2x^3 - 4x^2 - 3x +... (answered by nerdybill)

factor by grouping... (answered by jim_thompson5910)

Factor the expression: x^3 + 2x^2 - 3x - 6 (answered by rapaljer)

factor the expression:... (answered by Theo)