Chapter 8.5, Problem 3OE

a.

To determine

To find:

The remainder when given polynomial $P\left(x\right)$ is divided by the given binomials with the use of remainder theorem

Answer to Problem 3OE

The remainder of $P\left(x\right)=x^3-2x^2-x+2$ is 0

Explanation of Solution

Given information:

The polynomial is $P\left(x\right)=x^3-2x^2-x+2$

The binomial is $x-1$

Calculation:

The remainder can be obtained when $P\left(x\right)$ is divided by $x-1$ by evaluating $P\left(1\right)$

  $\begin{array}{l}P\left(1\right)={\left(1\right)}^3-2{\left(1\right)}^2-\left(1\right)+2\\ =1-2-1+2\\ =0\end{array}$

Therefore, the remainder of $P\left(x\right)=x^3-2x^2-x+2$ is 0

b.

To determine

To find:

The remainder when given polynomial $P\left(x\right)$ is divided by the given binomials with the use of remainder theorem

Answer to Problem 3OE

The remainder of $P\left(x\right)=x^3-2x^2-x+2$ is 0

Explanation of Solution

Given information:

The polynomial is $P\left(x\right)=x^3-2x^2-x+2$

The binomial is $x-2$

The remainder can be obtained when $P\left(x\right)$ is divided by $x-2$ by evaluating $P\left(2\right)$

  $\begin{array}{l}P\left(2\right)={\left(2\right)}^3-2{\left(2\right)}^2-\left(2\right)+2\\ =8-8-2+2\\ =0\end{array}$

Therefore, the remainder of $P\left(x\right)=x^3-2x^2-x+2$ is 0