Question

Use the remainder theorem to find P (1) for P (x) = - 2x4 + 423 - x+ 8.

Specifically, give the quotient and the remainder for the associated division and the value of P (1).
Quotient =
Remainder = [
P (1) =

Answer 1

To find P(1) for the polynomial P(x) = - 2x^4 + 423x^2 - x + 8 using the remainder theorem, divide the polynomial by x - 1 and evaluate it at x = 1. The quotient is - 2x^3 + 421x^2 + 421x + 429 and the remainder is 1. Therefore, P(1) = 428.

Step-by-step explanation:

To find P(1) using the remainder theorem for the polynomial P(x) = - 2x^4 + 423x^2 - x + 8, we divide the polynomial by x - 1 and evaluate it at x = 1.

Perform synthetic division, using 1 as the divisor and the coefficients of the polynomial as the dividend. The result is - 2x^3 + 421x^2 + 421x + 429.

The quotient is - 2x^3 + 421x^2 + 421x + 429 and the remainder is 1.

Evaluate P(1) by substituting x = 1 into the original polynomial: P(1) = - 2(1)^4 + 423(1)^2 - 1 + 8 = - 2 + 423 - 1 + 8 = 428.