Polynomials
Operations with polynomials
Start with the basics and progress through 9 lessons. Each lesson builds on the previous one.
0 of 9 lessons done
Test Your Knowledge
10 questions, new mix each time (from 151)
In This Topic (9 lessons)
Introduction to Polynomials
Learn what polynomials are, how to identify their parts, and classify them by degree and number of terms.
FOIL Method
Learn the FOIL method to multiply two binomials quickly and accurately.
Adding and Subtracting Polynomials
Learn how to add and subtract polynomials by combining like terms.
Classifying Polynomials
Learn to identify and classify polynomials by their degree and number of terms.
Multiplying Polynomials
Learn how to multiply polynomials using the distributive property and FOIL method.
Special Products
Learn the patterns for squaring binomials and multiplying conjugates to multiply polynomials faster.
Dividing Polynomials
Master polynomial division using long division, synthetic division, and factoring techniques.
Synthetic Division
Learn a faster method for dividing polynomials by linear factors using synthetic division.
Remainder Theorem
Learn how to find the remainder when dividing a polynomial by a linear factor without performing long division.
Polynomials are expressions containing variables raised to whole number powers. They are the workhorses of algebra, appearing in everything from simple area calculations to complex modeling in physics and engineering. Understanding polynomials is essential for calculus, where they serve as building blocks for understanding more complex functions.
In this topic, you will learn to classify polynomials by degree and number of terms. You will add, subtract, and multiply polynomials, mastering techniques like the distributive property and FOIL method. Polynomial division—both long division and synthetic division—extends your ability to work with these fundamental expressions.
Our lessons emphasize pattern recognition and strategic thinking. You will see how polynomials model real situations, from projectile motion to business profit functions. With practice, you will develop fluency in polynomial operations that prepares you for factoring, graphing, and solving polynomial equations.
What You'll Learn
- Classify polynomials by degree and number of terms
- Add and subtract polynomials by combining like terms
- Multiply polynomials using the distributive property
- Apply the FOIL method for binomial multiplication
- Perform polynomial long division
- Use synthetic division for division by linear factors
- Evaluate polynomials using substitution
Frequently Asked Questions
What is the degree of a polynomial?
The degree is the highest power of the variable in the polynomial. For example, 3x⁴ + 2x² - x + 5 has degree 4. The degree tells you about the polynomial behavior and number of possible roots.
What is the difference between a monomial, binomial, and trinomial?
These describe the number of terms: a monomial has 1 term, a binomial has 2 terms, and a trinomial has 3 terms. Any polynomial with 4+ terms is just called a polynomial.
When do I use synthetic division vs. long division?
Synthetic division is a shortcut that only works when dividing by a linear factor (x - c). For division by other polynomials, use long division. Synthetic division is faster once you learn the pattern.