Use synthetic division and the Remainder Theorem to evaluate P(c),

Question

where P(x)=x²+8x+10,c=−1. What is the answer and remainder? 

Answer 1

The Function is P(x) = x² + 8x + 10 and c = -1.

We solve this equation using synthetic division.

Synthetic Division of P(x) = x² + 8x + 10 with divisor c = -1 is

the polynomial is written as P(x) = (x-c) q(x) + r(x)

Then P(x) = (x+1) (x+7) + 3

Therefore using synthetic division, the remainder is r(x) = 3.

We find the remainder of the Function using Remainder theorem.

Remainder theorem of P(x) = x² + 8x + 10 with c = -1 is

P(-1) = (-1)² + 8(-1) + 10

P(-1) = 1 -8 + 10

P(-1) = 3

Therefore using Remainder theorem, the remainder is 3.