Given h(x) = x-3 and f(x) = x3-x2-x-15 is h(x) a factor of f(x)?

Accepted Solution

Answer:Yes. Step-by-step explanation:To see if h is a factor of f, we can use the factor theorem.h(x)=x-3 has a zero at x=3 because h(3)=3-3=0.So we want to see if the zero of h is a zero of f.Is x=3 a zero of f?You can check using synthetic division or just plug in 3.Let's do both.If you use synthetic you are trying to see if you get a remainder of 0.If you plug it in you are trying to see if you get 0 as the output when plugging your input 3.Let's do synthetic first:Since we are checking to see if x=3 is a zero, that will go on the outside:3 |  1   -1  -1   -15  |        3   6    15 - ------------------------      1    2   5     0So yep the remainder is 0 so the answer is yes.Let's plug it in:f(3)=3^3-3^2-3-15f(3)=27-9-3-15f(3)=18-3-15f(3)=15-15f(3)=0The result is 0 so the answer is yes.You pick your favorite way here.