I need help with this question.

Question

Given a polynomial f(x) the quotient f(x)/(x-5) has a remainder of 20. What is the value of f(5)?

Answer 1

previous answer by Paul is correct ----

since his R(x) is given as a constant for this problem

if F(x) polynomial, F(x)/[x-r]=H(x)+F(r)/[x-r]

dividing F(x)=xⁿ+a₁x^n-1+...+a_n-1x+a_n by (x-r)

where F(r)=constant and is in fact value of F at x=r

So F(x)=H(x)(x-r)+F(r)

(a bit different than Paul's answer)

It is kind of fun

let F(x)=x³+x-2,,,,,,and r=5

F(x)/[x-5]=x²+5x+26+128/[x-5]

immediately can conclude F(5)=128

for your problem, f(x)/[x-5]=g(x)+20/[x-5]

assuming f(x) is a polynomial

f(5) you can conclude is 20.

Answer 2

A polynomial p(x) can always be written as (x-r)*q(x)+R(x).

Then it is easy to see that p(r)=R(r).

This is the information you need to answer this question.