Q. 503 - Intermediate Algebra

Question

(a) Is it a monomial, binomial, or trinomial?

(b) What is its degree? 

$\left(m+3\right)\left(7m-2\right)$

Step-by-Step Solution

Answer

The given polynomial is a trinomial of degree 2.

Step 1. Given Information

The given polynomial is $\left(m+3\right)\left(7m-2\right)$.

Part (a) Step 1. Count the Terms in Simplified Polynomial

• Simplify the given expression as follows:

$\begin{array}{rcl}\left(m+3\right)\left(7m-2\right)& =& \left(m\times 7m\right)-\left(m\times 2\right)+\left(3\times 7m\right)-\left(3\times 2\right)\\ & =& 7m^2-2m+21m-6\\ & =& 7m^2+19m-6\\ & & \end{array}$

• As the polynomial has three terms, so it is a trinomial.

Part (b) Step 1. Find the Highest Power

• The term with highest power of the variable in the simplified polynomial is $7m^2$
• The exponent of this term is 2.
• So the degree of the trinomial is 2.