Question

Use the Factor Theorem to determine if the given binomial is a factor of the given polynomial function:f(x)=4x^4-20x^3+33x^2-22x+5;x-5/2

A:f(-5/2)≠0; the binomial is not a factor of the polynomial

B: f(5/2)≠0; the binomial is not a factor of the polynomial

C:f(-5/2)=0; yes, the binomial is a factor of the polynomial

D: f(5/2)=0; yes, the binomial is a factor of the polynomial

Answer 1

D: f(5/2)=0; yes, the binomial is a factor of the polynomial

Explanation:

The easy way to determine is to plug in the potential zero into the polynomial given the binomial divisor and see if it results in 0. If so, then the binomial is a factor of the polynomial:

Because f(5/2)=0, then the binomial is indeed a factor of the polynomial!