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.

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