Question

What is the remainder R when the polynomial p(x) is divided by (x-5)?
p(x) = x^3 - 5x^2 + 2x - 10

Answer 1

The question is an illustration of remainder theorem

The remainder of $\mathbf{P(x) = x^3 - 5x^2 + 2x - 10}$ divided by $\mathbf{x - 5}$ is 0

The polynomial is given as:

$\mathbf{P(x) = x^3 - 5x^2 + 2x - 10}$

The divisor is given as:

$\mathbf{x - 5}$

First, we set the divisor to 0

$\mathbf{x - 5 = 0}$

Solve for x

$\mathbf{x = 5}$

Substitute 5 for x in the polynomial

$\mathbf{P(x) = x^3 - 5x^2 + 2x - 10}$

$\mathbf{P(5) = 5^3 - 5 \times 5^2 + 2 \times 5 - 10}$

$\mathbf{P(5) = 125 - 125 + 10 - 10}$

$\mathbf{P(5) = 0}$

The above equation means that:

The remainder of $\mathbf{P(x) = x^3 - 5x^2 + 2x - 10}$ divided by $\mathbf{x - 5}$ is 0

Read more about remainder theorem at:

https://brainly.com/question/4782198