2x 3 4x 2 8x

Question 663778: Factor the polynomial? 2x^3+4x^2+8x
Answer by jim_thompson5910(35256)

(Show Source):

Yous tin can put this solution on YOUR website!

2x%5E3%2B4x%5E2%2B8x Start with the given expression.

2x%28x%5E2%2B2x%2B4%29 Factor out the GCF .

Now permit's try to factor the inner expression x%5E2%2B2x%2B4

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

Looking at the expression x%5E2%2B2x%2B4 , we can see that the starting time coefficient is , the second coefficient is , and the last term is .

At present multiply the first coefficient past the last term to get %281%29%284%29=4 .

At present the question is: what two whole numbers multiply to (the previous production)

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 :
ane,2,four
-1,-two,-4

Note: list the negative of each factor. This volition allow u.s.a. to find all possible combinations.

These factors pair upwardly and multiply to .
1*4 = 4
two*2 = four
(-1)*(-4) = 4
(-two)*(-2) = 4

Now allow's add up each pair of factors to meet if i pair adds to the center coefficient :

From the table, we can run into that there are no pairs of numbers which add to . Then x%5E2%2B2x%2B4 cannot be factored.

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

Answer:

So 2x%5E3%2B4x%5E2%2B8x simply factors to 2x%28x%5E2%2B2x%2B4%29

In other words, 2x%5E3%2B4x%5E2%2B8x=2x%28x%5E2%2B2x%2B4%29 .

2x 3 4x 2 8x,

Source: https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Polynomials-and-rational-expressions.faq.question.663778.html