Question

Use long division and the Remainder Theorem to evaluate P(c), where:P(x)= x^3-8x^2+17x-16, c=2The quotient is: ______The remainder is: ______P(c)= _______

Answer 1

Given,

The expression is,

$P\mleft(x\mright)=x^3-8x^2+17x-16$

Here, c=2

According to remainder theorem when divide a polynomial

by a binomial of degree (x-c) then the reminder is p(c).

Substituting c=2,

By long division method,

The quotient is : x^2-6x+5

The reminder is : -6

P(c)=P(2)=-6

Hence, the quotient and reminder of the polynomial is x^2-6x+5 and -6 respectively.