Chapter 8.1, Problem 3P

a.

To determine

To find: name and degree of the given polynomial

Answer to Problem 3P

Degree is $2$

Name of the polynomial based on degree is quadratic polynomial.

Name of the polynomial based on number of terms is trinomial

Explanation of Solution

Given information: Polynomial is $2x-3+8x^2$

A polynomial is said to be in standard form if the terms of the polynomial are arranged from term of highest degree to the terms of lowest degree.

Exponent refers to the power of the variable.

Given polynomial is $2x-3+8x^2$

Standard form is $8x^2+2x-3$

Degree refers to the highest power of the variable

So, degree of the polynomial $2x-3+8x^2$ is $2$

A polynomial of degree $2$ is known as a quadratic polynomial

Also,

Number of terms in the polynomial $2x-3+8x^2$ is $3$

A polynomial with $3$ terms is known as a trinomial.

b.

To determine

To explain: how writing a polynomial in standard form helps to name the polynomial

Explanation of Solution

As a polynomial is written in standard form, it helps to know quickly the highest power of the variable that is the degree of the polynomial.

As we write the polynomial in standard form as $8x^2+2x-3$ ,

We can very easily find the degree of the polynomial.