Question

Determine whether each expression is a polynomial. If so, identify the polynomial as a monomial, binomial, or trinomial.

$4t^5+3t^2+t$

Short answer

The given expression$4t^5+3t^2+t$ is a polynomial. The given polynomial$4t^5+3t^2+t$ is a trinomial.

Step-by-step solution

Step 1. Write the definition of the polynomial.

A monomial is a number, a variable or the product of a number and one or more variables with non-negative integer exponents. The monomial has only one term.

A polynomial is a monomial or the sum of monomials, each called a term of the polynomial.

The polynomial having only one term is called a monomial.

The polynomial having two terms is called a binomial. That is binomial is sum of two monomials.

The polynomial having three terms is called a trinomial. That is trinomial is sum of three monomials.

Step 2. Determine whether each expression is a polynomial.

The given expression is$4t^5+3t^2+t$.

It can be noticed that each term of the given expression is a variable or the product of a number and one variable with non-negative integer exponents.

Therefore, each term of the given expression is a monomial.

As, the given expression is the sum of the monomials. Therefore, the given expression is a polynomial.

 Step 3. Identify the polynomial as a monomial, binomial, or trinomial.

The given expression is a polynomial having three terms that is the given polynomial is sum of three monomials.

Therefore, the given polynomial $4t^5+3t^2+t$is a trinomial.