# How do you determine the binomial factors of #x^3-5x^2+2x+8#?

##### 1 Answer

Dec 28, 2016

#### Explanation:

Given:

#x^3-5x^2+2x+8#

Notice that if we reverse the signs on the coefficients of the terms with odd degree then the sum of the coefficients is zero.

That is:

#-1-5-2+8 = 0#

Hence

#x^3-5x^2+2x+8 = (x+1)(x^2-6x+8)#

To factor the remaining quadratic note that

#x^2-6x+8 = (x-4)(x-2)#

Putting it all together:

#x^3-5x^2+2x+8 = (x+1)(x-4)(x-2)#