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Degree of a Polynomial

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Degree of a Polynomial

Study Guide

Key Definition

The degree of a polynomial is the greatest of the degrees of its terms after simplification. For example, in the polynomial $x^7 + 2x^3 + 6x - x^7$, it simplifies to $2x^3 + 6x$, and the degree is 3.

Important Notes

The degree of a monomial is the sum of the exponents of all its variables.
A constant has a degree of 0.
Simplify the polynomial before finding its degree.
The degree of $7y^3z^2$ is 5 (since $3 + 2 = 5$).
The degree of $66$ is 0.

Mathematical Notation

$x^n$ denotes x raised to the power of n

$\frac{a}{b}$ represents division

$+$ represents addition

$-$ represents subtraction

$x^{-n}$ denotes x raised to a negative exponent

Remember to use proper notation when solving problems

Why It Works

The degree of the polynomial helps in understanding the behavior of the polynomial function, particularly its end behavior and the number of roots it can have.

Remember

The highest power of the variable in a polynomial gives its degree.

Quick Reference

Degree of Monomial:$\text{sum of exponents}$

Degree of Polynomial:$\text{highest degree of terms}$

Understanding Degree of a Polynomial

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

The degree of a polynomial is the largest degree of any term (for multivariable terms, the sum of its exponents).

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the degree of the monomial $3x^2y^4$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

You are designing a skateboard ramp, and the polynomial $4x^3 + 5x^2 - 3$ describes the curve. What is the degree of the polynomial?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Consider the polynomial $x^4 + x^2y^2 + y^4$. What is its degree?

Challenge Quiz

Single Choice Quiz

Advanced

Given the polynomial $x^5y^2 + x^3y^4 + xy$, find its degree.

Recap

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Review key concepts and takeaways