Use the factor theorem to determine if the given binomial is a factor of f (x).
-$$f ( x ) = 2 x ^ { 3 } + x ^ { 2 } - 9 x - 6 ; x - 1$$
A) No
B) Yes

Question

Quizplus · Accepted Answer

The factor theorem states that $ x - c $ is a factor of $ f(x) $ if and only if $ f(c) = 0 $. Substituting $ x = 1 $ into $ f(x) $, we get $ f(1) = 2(1)^3 + (1)^2 - 9(1) - 6 = 2 + 1 - 9 - 6 = -12 $, which is not zero. Therefore, $ x - 1 $ is not a factor of $ f(x) $.

Use the Factor Theorem to Determine If the Given Binomial f(x)=2x3+x2−9x−6;x−1f ( x ) = 2 x ^ { 3 } + x ^ { 2 } - 9 x - 6 ; x - 1f(x)=2x3+x2−9x−6;x−1

Use the Factor Theorem to Determine If the Given Binomial $f ( x ) = 2 x ^ { 3 } + x ^ { 2 } - 9 x - 6 ; x - 1$