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Adding and Subtracting Polynomials

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Adding and Subtracting Polynomials

Study Guide

Key Definition

A polynomial is an expression made up of one or more terms, each term being a coefficient multiplied by variables raised to non-negative integer exponents, where terms are combined using addition and subtraction. Division by a variable is not allowed. Depending on how many terms an expression has, it is called a monomial, binomial, trinomial, or polynomial.

Important Notes

Each term of a polynomial is a part of the expression generally separated by '+' or '-' signs.
The highest exponent on a variable in a polynomial tells us its degree.
Constant terms in a polynomial do not have a variable but can be considered as having an implied variable with an exponent of zero.

Mathematical Notation

$x^n$ - a variable x raised to the power n, where n is a non-negative integer

$c$ - a constant term (coefficient)

$3x^2 + 5x^2 = 8x^2$ - example of combining like terms

Remember to use proper notation when solving problems. In polynomials, exponents must be non-negative integers.

Why It Works

In adding or subtracting polynomials, we simply combine or subtract like terms. Like terms are terms with the same variables and powers.

Remember

When adding or subtracting polynomials, always combine like terms.

Quick Reference

Adding Polynomials:$x^n + x^n$

Subtracting Polynomials:$x^n - x^n$

Understanding Adding and Subtracting Polynomials

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

A polynomial is an expression made by adding or subtracting terms, where each term consists of a coefficient multiplied by a variable raised to a non-negative integer exponent. To add or subtract polynomials, combine the coefficients of like terms (terms with the same variable and exponent).

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the degree of the polynomial $3x^2 + 5 - 4y$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

You are helping your little brother with his math homework. He needs to add the polynomials $2x^2 + 3x + 1$ and $5x^2 - x + 4$. What is the sum?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

What is the degree of the polynomial that is the sum of the polynomials $3x^2 + 5 - 4y$ and $2x^3 + 7x^2 + 1$?

Challenge Quiz

Single Choice Quiz

Advanced

What is the result of subtracting the polynomial $3x^2 + 2x - 4$ from the polynomial $2x^3 + x^2 + x + 1$?

Recap

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