Use the factor theorem to determine whether the binomial x + 1 is a factor of the polynomial function ? (x) = 2x3 – 9x2 + 17x – 6.

(x + 1 ) is not a factor of the polynomial

given (x - a) is a factor of a polynomial f(x) then x = a is a root and the remainder is f(a) = 0

evaluate the polynomial f(- 1)

f(- 1) = 2(- 1)³ - 9(- 1)² + 17(- 1) - 6

       = - 2 - 9 - 17 - 6 = - 34 ≠ 0

Thus (x + 1) is not a factor of the polynomial

answer

the correct answer is

explanation

the given function is

the excluded values are obtained by solving:

we factor to obtain:

the excluded values are