Question

Identify the binomial that is not a factor of the polynomial P(X) = 3X^3 + 5X^2 - 4X - 4.

Answer 1

To identify the binomial that is not a factor of the given polynomial, we can use the Remainder Theorem and plug each binomial as a factor into the polynomial.

Step-by-step explanation:

In this question, we need to identify the binomial that is not a factor of the given polynomial. To do this, we can use the Remainder Theorem. According to the Remainder Theorem, if a polynomial P(X) is divided by a binomial (X - a), the remainder will be equal to P(a).

Let's check each binomial as a factor:

1. (X + 1): P(-1) = 3(-1)^3 + 5(-1)^2 - 4(-1) - 4 = -3 + 5 + 4 - 4 = 2.
2. (X - 2): P(2) = 3(2)^3 + 5(2)^2 - 4(2) - 4 = 24 + 20 - 8 - 4 = 32.
3. (X + 4): P(-4) = 3(-4)^3 + 5(-4)^2 - 4(-4) - 4 = -192 + 80 + 16 - 4 = -100.

From the calculations above, we can see that the binomial (X + 1) is not a factor of the polynomial P(X).