Chapter 4.1, Problem 12WE

a.

To determine

Add the polynomial $2n^2-n+5$ to the polynomial $n^2+1$ .

Answer to Problem 12WE

The addition of the polynomials is $3n^2-n+6$ .

Explanation of Solution

Given information: The given polynomials are $2n^2-n+5$ and $n^2+1$ .

Calculation: Add the polynomial $2n^2-n+5$ to the $n^2+1$ .

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

b.

To determine

Subtract the polynomial $n^2+1$ from $2n^2-n+5$ .

Answer to Problem 12WE

The subtraction of polynomial $n^2+1$ from $2n^2-n+5$ is $n^2-n+4$ .

Explanation of Solution

Given information: The given polynomials are $2n^2-n+5$ and $n^2+1$ .

Calculation: Subtract the polynomial $n^2+1$ from $2n^2-n+5$ .

  $\begin{array}{c}\left(2n^2-n+5\right)-\left(n^2+1\right)=\left(2n^2-n^2\right)+\left(-n\right)+\left(5-1\right)\\ =n^2-n+4\end{array}$