Question

classify the polynomial as a monomial, binomial, trinomial, or none of these. also, give the degree.
$x^2 - 6x + 9$
choose the correct type of polynomial
\bigcirc binomial
\bigcirc monomial
\bigcirc trinomial
\bigcirc none of these

Explanation:

Step1: Identify the number of terms

A term is a single number, variable, or product of numbers and variables. In the polynomial \(x^2 - 6x + 9\), the terms are \(x^2\), \(-6x\), and \(9\). So there are 3 terms.

Step2: Classify the polynomial by number of terms

• A monomial has 1 term.
• A binomial has 2 terms.
• A trinomial has 3 terms.

Since this polynomial has 3 terms, it is a trinomial.

Step3: Find the degree of the polynomial

The degree of a polynomial is the highest power of the variable. In \(x^2 - 6x + 9\), the highest power of \(x\) is 2 (from the term \(x^2\)).

Answer:

The polynomial \(x^2 - 6x + 9\) is a trinomial with degree 2. For the given options (Binomial, Monomial, Trinomial, None of these), the correct option is: Trinomial (assuming the options include Trinomial; if the visible options in the image are as shown with Binomial, Monomial, Trinomial, None of these, then the answer is the option corresponding to Trinomial, e.g., if the options are labeled as: Binomial, Monomial, Trinomial, None of these, then the answer is the option with "Trinomial" text).