Question

Use the Remainder Theorem to evaluate factors of polynomialsSuppose you were given the function F(x) = x⁴− 2x³+ 3x² −10+3and the factor (x − 2). What is the value of a (x-a)Use the Remainder Theorem to solve whether or not (x − 2) is a factor F(x)=x⁴-2x³+3x²−10x+2

Answer 1

Given:

$f(x)=x^4-2x^3+3x^2-10x+2$

Requirement:

To check whether (x-2) is a factor of a given equation or not using remainder method.

Explanation:

By putting x = 2 in the given equation we get

$\begin{gathered} f(2)=2^4-2(2)\placeholder{⬚}^3-3(x)\placeholder{⬚}^2-10(2)+2 \\ =-6 \end{gathered}$

Since f(2) = -6 it meant it will give -6 as a remainder after dividing the equation by (x - 2)

Hence, (x - 2) is not a factor of the given equation.

Final Answer:

(x - 2) is not a factor of the given equation.