Use the Remainder Theorem to evaluate P(c).

Question

P(x) = x⁴ − 8x² + 13,     c = 2

Answer 1

use long or synthetic division

2| 1 -8 0 13

2 -12 -24

1-6 -12

-11

x^3-8x^2+13 divided by x-2 = x^2-6x-12 with remainder -11

P(2) = the remainder = -11

check the answer:

p(2)=2^3-8(2)^2+13 = 8-32+13 = -11