Question

Is (x − 6) a factor of f(x) = x3 − 3x2 + 2x − 8? Use either the remainder theorem or the factor theorem to explain your reasoning.

Answer 1

Below.

Explanation:

If x - 6 is a factor of f(x) then f(6) will be zero.

So we substitute x = 6 into the function:

f(6) = (6)^3 - 3(6)^2 + 2(6) - 8

= 216 - 108 + 12 - 8

= 112.

So f(6) is not zero and x - 6 is not a factor.