Using the remainder theorem to evaluate a polynomial

Question

Use the remainder theorem to find P(-1) for P(x) = -2x^4 - 2x^3 + 2x + 5.

Specifically, give the quotient and the remainder for the associated division and the value of P(-1).

QUOTIENT = ?

REMAINDER = ?

P(-1) = ?

Answer 1

P(-1) =-2(-1)^4 -2(-1)^3 +2(-1) +5 = -2+2-2+5 =3 = remainder

P(-1) =3

remainder = P(-1) = 3

quotient = -2x^3 +2

use long or synthetic division

divide x+1 into -2x^4 -2x^3 +2x +5

for synthetic division

-1 | -2 -2 2 5

____2 0 -2

-2 0 2 3

-2, 0, 2 are the coefficients of the quotient for x^2, x and the constant term

-2x^2 + 0x + 2 = -2x^2 +2

the 3 is the remainder