SOLUTION: Let f(x) be a polynomial such that f(0) = 4, f(1) = 6, and f(2) = -2. Find the remainder when f(x) is divided by x.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Let f(x) be a polynomial such that f(0) = 4, f(1) = 6, and f(2) = -2. Find the remainder when f(x) is divided by x.      Log On


   

Question 1209682: Let f(x) be a polynomial such that f(0) = 4, f(1) = 6, and f(2) = -2. Find the remainder when f(x) is divided by x.
Answer by math_tutor2020(3817) About Me  (Show Source):
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Answer: 4

Explanation
Think of "divided by x" as "divided by x-0"
Comparing x-0 with x-k shows k = 0

Remainder Theorem:
When dividing p(x) over (x-k), the remainder is p(k)

This means we go with f(0) = 4

A slightly more in-depth look:
f(x)/g(x) = quotient + remainder/g(x)
f(x) = g(x)*quotient + remainder
f(x) = x*quotient + remainder
f(0) = 0*quotient + remainder
f(0) = remainder = 4