SOLUTION: Factor the polynomial? 2x^3+4x^2+8x

Question 663778: Factor the polynomial? 2x^3+4x^2+8x
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 :
1,2,4
-1,-2,-4

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

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

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	4	1+4=5
2	2	2+2=4
-1	-4	-1+(-4)=-5
-2	-2	-2+(-2)=-4

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
for the polynomial -2x^3-4x^2+8x A) Factor out -2x B) Factor out... (answered by MathLover1)

Factor the Polynomial... (answered by ankor@dixie-net.com)

Factor the polynomial {{{-2x^3+12x^2+8x-48}}} using the factor... (answered by MathLover1)

Factor... (answered by Alan3354)

factor the polynomial completely... (answered by Edwin McCravy)

Factor the polynomial... (answered by jrfrunner)

factor each expression: 8x^3 + 4x^2 -... (answered by jim_thompson5910)

factor: 2x^5 + x^4 - 8x^3 -... (answered by stanbon,nerdybill,MathTherapy)

Factor out the greatest common factor from each polynomial. 1. 6x^7+3x^4-9x^2 2.... (answered by ikleyn)