Answer:
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.
