Chapter 7.6, Problem 50HP

To determine

The steps to multiply a polynomial by a monomial.

Explanation of Solution

To multiply a polynomial by a monomial, multiply each term of polynomial with that monomial.

1. Write the monomial and the polynomial in the same row.
2. Now, expand and multiply each term of the polynomial by the monomial.

For example:

  $\begin{array}{l}{\text{Multiply 5n and 2n}}^2+2n+1\\ =5n\times \left({\text{2n}}^2+2n+1\right)\left[\text{Write both in same row}\right]\\ =10n^3+10n^2+5n\left[\text{Expand polynomial and multiply each term with monomial}\right]\end{array}$