High School

When the function [tex]f(x) = x^4 + 2x^3 + 4x^2 + x - 1[/tex] is divided by [tex](x - 2)[/tex], the result is [tex]x^3 + 4x^2 + 12x + 25[/tex] with a remainder of 49. Which conclusion is valid?

A. [tex]f(-2) = 49[/tex]
B. [tex]f(49) = -2[/tex]
C. [tex]f(2) = 49[/tex]
D. [tex]f(49) = 2[/tex]

Answer :

The remainder when the function f(x) = x⁴ + 2x³ + 4x² + x - 1 is divided by (x - 2) to get x³ + 4x² + 12x + 25 is 49. Therefore f(2) = 49

What is an equation?

An equation is used to show the relationship between numbers and variables.

Polynomial is an expression composed of variables, constants and exponents using mathematical operations such as addition, subtraction, multiplication and division.

The remainder theorem states that when a polynomial f(x) is divided by (x - a), it gives a remainder equal to f(a).

Given that f(x) = x⁴ + 2x³ + 4x² + x - 1 is divided by (x - 2) to get x³ + 4x² + 12x + 25 with a remainder of 49

Applying the remainder theorem to the above polynomial:

x - 2 = 0

x = 2

Hence:

f(2) = 49

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