Question

Select the correct answer.

Using the remainder theorem, which quotient has a remainder of 20?
.
OA. (x^3 + 5x^2 - 4x + 6) = (x + 5)
B. (3x^3 + 7x^2 + 5x + 2) = (x - 2)
OC. (x^4 – 8x^2 + 16) = (x + 4)
OD. (3x^4 – 5x^3 + 5x + 2) = (x - 2)

Answer 1

Explanation:

the remainder theorem data that for a division of f(x) by (x - r), the remainder of this division is f(r).

A. r = -5

f(-5) = (-5)³ + 5×(-5)² - 4×-5 + 6 = -20 + 6 = -14 and not 20

B. r = 2

f(2) = 3×2³ + 7×2² + 5×2 + 2 = ... definitely larger than 20

C. r = -4

f(-4) = (-4)⁴ - 8×(-4)² + 16 = 256 - 128 + 16 = 144 and not 20

D. r = 2

f(2) = 3×2⁴ - 5×2³ + 5×2 + 2 = 48 - 40 + 10 + 2 = 20

so, D is correct.