Select all polynomials that are divisible by (x + 1).

Choose all answers that apply:

A. A (x) = x^4 - 3x^3 - 4

B. B (x) = x^4 + 2x + 1

C. C (x) = x^3 - 3x^2 + 4x - 2

D. D (x) = 2^3 + 2x^2 - 5x - 6

A. and B.

Step-by-step explanation:

The binomial x + 1 divides the polynomial ƒ (x) only if x = - 1 is a root of the polynomial, i. e., f (-1) = 0.

So, we must evaluate f (-1) for each polynomial.

A. A (x) = x⁴ - 3x³ - 4

A (-1) = (-1) ⁴ - 3 (-1) ³ - 4 = 1 - 3 (-1) - 4 = 1 + 3 - 4 = 0. Divisible by x + 1.

B. B (x) = x⁴ + 2x + 1

B. B (-1) = (-1) ⁴ + 2 (-1) + 1 = 1 - 2 + 1 = 0. Divisible by x + 1.

C. C (x) = x³ - 3x² + 4x - 2

C (-1) = (-1) ³ - 3 (-1) ² + 4 (-1) - 2 = - 1 - 3 (1) - 4 - 2 = - 1 - 3 - 4 - 2 = - 10. Not divisible by x + 1.

D. D (x) = 2x³ + 2x² - 5x - 6

D (-1) = 2 (-1) ³ + 2 (-1) ² - 5 (-1) - 6 = 2 (-1) + 2 (1) - (-5) - 6 = - 2 + 2 + 5 - 6 = - 1. Not divisible by x + 1.