Suppose f(x) is a polynomial of degree 4 or greater such that f(1) = 2, f(2) = 3, and f(3) = -4. Find the remainder when f(x) is divided by (x - 1)(x - 2)(x - 3).

Guest Feb 2, 2022

#1**0 **

f(x) is a polynomial of degree 4 or greater such that f(1) = 2, f(2) = 3, and f(3) = -4.

Find the remainder when f(x) is divided by (x - 1)(x - 2)(x - 3).

f(x) = P(x)*(x - 1)(x - 2)(x - 3) + R(x) where P(x) is some polynomial and R(x) is the remainder ax^{2} + bx + c

f(x) = P(x)*(x - 1)(x - 2)(x - 3) + (ax^{2} + bx + c)

f(1) = a + b + c = 2

f(2) = 4a + 2b + c = 3

f(3) = 9a +3b + c = -4

Solving for a, b , c => a = -4, b = 13, c = -7

R(x) = -4x^{2 }+ 13x - 7.

Guest Feb 3, 2022