use the Factor Theorem to determine whether x-2 is a factor of f(x)=3x^4-6x^3-5x+10. Give a written explanation as to why x-2 is or is not a factor.

Question

use the Factor Theorem to determine whether x-2 is a factor of f(x)=3x^4-6x^3-5x+10. Give a written explanation as to why x-2 is or is not a factor.

Answer 1

if x-2 is a factor then x=2 is a root or zero of the polynomial

f(2)=3(2^4)-6(2^3)-5(2)+10

f(2)=3*16-6*8-5(2)+10

f(2)=48-48-10+10

f(2)=0 so 2 is a root and x-2 is a factor of f(x)