Which polynomial is not a factor of 3x4 – 16x3 – 3x2 + 36x + 20?AnswersA.x – 1B.x – 5C.x + 1D.3x + 2

To determine which polynomial is not a factor of the given polynomial, we can use the Factor Theorem. The Factor Theorem states that a polynomial f(x) has a factor (x - k) if and only if f(k) = 0.

Let's test each of the given options:

A. x – 1: Substitute x = 1 into the polynomial. If the result is zero, then x - 1 is a factor. 3(1)^4 - 16(1)^3 - 3(1)^2 + 36(1) + 20 = 3 - 16 - 3 + 36 + 20 = 40 ≠ 0. So, x - 1 is not a factor.

B. x – 5: Substitute x = 5 into the polynomial. If the result is zero, then x - 5 is a factor. 3(5)^4 - 16(5)^3 - 3(5)^2 + 36(5) + 20 = 1875 - 2000 - 75 + 180 + 20 = 0. So, x - 5 is a factor.

C. x + 1: Substitute x = -1 into the polynomial. If the result is zero, then x + 1 is a factor. 3(-1)^4 - 16(-1)^3 - 3(-1)^2 + 36(-1) + 20 = 3 + 16 - 3 - 36 + 20 = 0. So, x + 1 is a factor.

D. 3x + 2: Substitute x = -2/3 into the polynomial. If the result is zero, then 3x + 2 is a factor. 3(-2/3)^4 - 16(-2/3)^3 - 3(-2/3)^2 + 36(-2/3) + 20 = 0. So, 3x + 2 is a factor.

Therefore, the polynomial that is not a factor of the given polynomial is A. x - 1.