Question

Use the Remainder Theorem to find the remainder of 2x4+x2-10x-1 by x+2.

Answer 1

Remainder Theorem: for divisor x + 2, take a = -2 and compute f(-2).

f(x) = 2x^4 + x^2 - 10x - 1
f(-2) = 2(−2)^4 + (−2)^2 − 10(−2) − 1
= 2(16) + 4 + 20 − 1
= 32 + 4 + 20 − 1 = 55

Remainder = 55.