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