Question

Which of the following binomials is a factor of x^3+4x^2+x-6?

Answer 1

(x-1)(x+2)(x+3) 

This is how you would factor it out.

Answer 2

Answer:

(x-1), (x+2) and (x+3) are factors of given polynomial.

Step-by-step explanation:

The given expression is

$x^3+4x^2+x-6$

It can be rewritten as

$x^3+(-x^2+5x^2)+(-5x+6x)-6$

$(x^3-x^2)+(5x^2-5x)+(6x-6)$

$x^2(x-1)+5x(x-1)+6(x-6)$

Taking out common factors.

$(x-1)(x^2+5x+6)$

Splitting the middle term in the parenthesis we get

$(x-1)(x^2+5x+6)$

$(x-1)(x^2+3x+2x+6)$

$(x-1)(x(x+3)+2(x+3))$

$(x-1)(x+2)(x+3)$

Therefore, (x-1), (x+2) and (x+3) are factors of given polynomial.