Question

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

(b) What is its degree?

${\left(4x-3\right)}^2$

Short answer

The given polynomial is a trinomial of degree 2.

Step-by-step solution

Step 1. Given Information

The given polynomial is${\left(4x-3\right)}^2$

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

• Simplify the given expression as follows:

$\begin{array}{rcl}{\left(4x-3\right)}^2& =& {\left(4x\right)}^2+{\left(-3\right)}^2-2\left(4x\right)\left(3\right)\\ & =& 16x^2+9-24x\end{array}$

• As the polynomial has 3 terms, 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 $16x^2$
• The exponent of this term is 2.
• So the degree of the trinomial is 2.