Chapter 4.1, Problem 17OE

a.

To determine

Add the polynomial $3r-5$ to the polynomial $r^2-2r+6$ .

Answer to Problem 17OE

The addition of the polynomials is $r^2+r+1$ .

Explanation of Solution

Given information: The given polynomials are $3r-5$ and $r^2-2r+6$ .

Calculation: Add the polynomial $3r-5$ to $r^2-2r+6$ .

  $\begin{array}{c}\left(3r-5\right)+\left(r^2-2r+6\right)=\left(3r-2r\right)+\left(-5+6\right)+\left(r^2\right)\\ =r+1+r^2\\ =r^2+r+1\end{array}$

b.

To determine

Subtract the polynomial $r^2-2r+6$ from $3r-5$ .

Answer to Problem 17OE

The subtraction of polynomial $r^2-2r+6$ from $3r-5$ is $-r^2+5r-11$ .

Explanation of Solution

Given information: The given polynomials are $3r-5$ and $r^2-2r+6$ .

Calculation: Subtract the polynomial $r^2-2r+6$ from $3r-5$ .

  $\begin{array}{c}\left(3r-5\right)-\left(r^2-2r+6\right)=\left(3r+2r\right)+\left(-5-6\right)+\left(-r^2\right)\\ =5r-11-r^2\\ =-r^2+5r-11\end{array}$