Question

Use the Factor Theorem to determine whether x-1 is a factor of P(x) = 2x³-3x²-9.

Specifically, evaluate P at the proper value, and then determine whether x − 1 is a factor.

Answer 1

Evaluating P(x) at x=1, we find that P(1) = -10, which is not zero. Therefore, x-1 is not a factor of the polynomial P(x) = 2x³-3x²-9 according to the Factor Theorem.

Step-by-step explanation:

To determine if x-1 is a factor of P(x) = 2x³-3x²-9, we use the Factor Theorem. The Factor Theorem states that (x - c) is a factor of a polynomial P(x) if and only if P(c)=0. In this case, we need to evaluate P(x) at x=1 because if (x - 1) is a factor, P(1) should equal to 0.

Let's evaluate P at x=1:

P(1) = 2(1)³ - 3(1)² - 9 = 2(1) - 3(1) - 9 = 2 - 3 - 9

P(1) = -10

Since P(1) is not equal to 0, x-1 is not a factor of P(x).