Chapter 4.1, Problem 18OE

a.

To determine

Add the polynomial $u^2-6u+7$ to the polynomial $u^2+6u-8$ .

Answer to Problem 18OE

The addition of the polynomials is $2u^2-1$ .

Explanation of Solution

Given information: The given polynomials are $u^2-6u+7$ and $u^2+6u-8$ .

Calculation: Add the polynomial $u^2-6u+7$ to $u^2+6u-8$ .

  $\begin{array}{c}\left(u^2-6u+7\right)+\left(u^2+6u-8\right)=\left(u^2+u^2\right)+\left(-6u+6u\right)+\left(7-8\right)\\ =2u^2+\left(0\right)-1\\ =2u^2-1\end{array}$

b.

To determine

Subtract the polynomial $u^2+6u-8$ from $u^2-6u+7$ .

Answer to Problem 18OE

The subtraction of polynomial $u^2+6u-8$ from $u^2-6u+7$ is $-12u+15$ .

Explanation of Solution

Given information: The given polynomials are $u^2-6u+7$ and $u^2+6u-8$ .

Calculation: Subtract the polynomial $u^2+6u-8$ from $u^2-6u+7$ .

  $\begin{array}{c}\left(u^2-6u+7\right)-\left(u^2+6u-8\right)=\left(u^2-u^2\right)+\left(-6u-6u\right)+\left(7+8\right)\\ =\left(0\right)-12u+15\\ =-12u+15\end{array}$