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

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

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.