SOLUTION: factor, (show all stages, result of factoring out a GCF before taking resulting polynomial and factoring it again)Check answer.3x^2+2x-8

Question 168712: factor, (show all stages, result of factoring out a GCF before taking resulting polynomial and factoring it again)Check answer.3x^2+2x-8
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

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 :
1,2,3,4,6,8,12,24
-1,-2,-3,-4,-6,-8,-12,-24

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

These factors pair up and multiply to .
1*(-24)
2*(-12)
3*(-8)
4*(-6)
(-1)*(24)
(-2)*(12)
(-3)*(8)
(-4)*(6)

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	-24	1+(-24)=-23
2	-12	2+(-12)=-10
3	-8	3+(-8)=-5
4	-6	4+(-6)=-2
-1	24	-1+24=23
-2	12	-2+12=10
-3	8	-3+8=5
-4	6	-4+6=2

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

So the two numbers and both multiply to and add to

Now replace the middle term with . Remember, and add to . So this shows us that .

Replace the second term with .

Group the terms into two pairs.

Factor out the GCF from the first group.

Factor out 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.

Combine like terms. Or factor out the common term

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

Answer:

So factors to .

Note: you can check the answer by FOILing to get or by graphing the original expression and the answer (the two graphs should be identical).

RELATED QUESTIONS
factor, (show all stages, result of factoring out a GCF before taking resulting... (answered by jim_thompson5910)

factor, show all stages(factoring out a GCF before taking resulting polynomial and... (answered by jim_thompson5910)

Show all stages of factoring separately (i.e., show the result of factoring out a GCF... (answered by stanbon)

factor, (show all stages, result of factoring out a GCF before taking resulting... (answered by jim_thompson5910)

Factor completely: x^10y^3 � 4x^9y^2 � 21x^8y If you believe that a polynomial is not (answered by stanbon)

Make sure to superscript all exponents. If you believe that a polynomial is not... (answered by Alan3354)

Make sure to superscript all exponents. If you believe that a polynomial is not... (answered by EMStelley)

Make sure to superscript all exponents. If you believe that a polynomial is not... (answered by Earlsdon)

Make sure to superscript all exponents. If you believe that a polynomial is not... (answered by jim_thompson5910)