Algebra Examples Simplifying Polynomials

Find the Degree, Leading Term, and Leading Coefficient

$x^{4} - 7 x^{2} - 1$

Step 1

The degree of a polynomial is the highest degree of its terms.

Tap for more steps...

Step 1.1

Identify the exponents on the variables in each term, and add them together to find the degree of each term.

$x^{4} \to 4$

$- 7 x^{2} \to 2$

$- 1 \to 0$

Step 1.2

The largest exponent is the degree of the polynomial.

$4$

Step 2

The leading term in a polynomial is the term with the highest degree.

$x^{4}$

Step 3

The leading coefficient of a polynomial is the coefficient of the leading term.

Tap for more steps...

Step 3.1

The leading term in a polynomial is the term with the highest degree.

$x^{4}$

Step 3.2

The leading coefficient in a polynomial is the coefficient of the leading term.

$1$

Step 4

List the results.

Polynomial Degree: $4$

Leading Term: $x^{4}$

Leading Coefficient: $1$

Enter YOUR Problem

Simplifying Polynomials

More step-by-step Algebra examples from this chapter.

How to Use Step-by-Step Examples

Read the worked problem

Each example starts from a real Algebra problem and shows the rule or formula it relies on.

Follow every step

Work through the solution line by line. Underlined terms open a glossary definition.

Solve your own problem

Enter a similar problem in the Algebra solver to get the answer with steps.

Why use Mathway?

Step-by-step solutions

See how every answer is worked out, not just the result.

Every major math subject

From basic math through calculus, statistics and chemistry.

Accurate results

Answers you can check your homework against.

Trusted by students

A reliable tool for homework and learning.

Find the Degree, Leading Term, and Leading Coefficient

Simplifying Polynomials

How to Use Step-by-Step Examples

Why use Mathway?

Explore More Algebra Help