Polynomials
Adding, subtracting, and multiplying polynomials (FOIL), and factoring (trinomials, GCF).
This page is a free outline of what the Polynomials lesson covers — it is not the lesson itself. The interactive lesson, practice, quizzes, and AI Tutor are inside the app.
This lesson covers
- Adding and Subtracting Polynomials To add or subtract polynomials, combine like terms: add or subtract the coefficients of terms with the same variable and exponent, and leave unlike terms as they are.
- Classifying Polynomials Polynomials are named by their number of terms — a monomial has one, a binomial two, a trinomial three — and by their degree, the highest exponent present.
- Combining Like Terms
- Distributive Property The distributive property says multiplying into parentheses multiplies every term inside: a(b + c) = ab + ac. So 3(x + 4) = 3x + 12 — the key move for clearing parentheses in algebra.
- Evaluating Expressions To evaluate an expression, substitute a number for each variable and compute using order of operations. Evaluating 3x + 5 at x = 4 gives 3(4) + 5 = 17.
- Factoring Out the GCF Factoring out the GCF pulls the greatest common factor of every term outside the parentheses: 6x³ + 9x becomes 3x(2x² + 3). It’s the first thing to check before any other factoring.
- Factoring the Difference of Squares A difference of squares — a² − b², two perfect squares with a minus between them — always factors as (a + b)(a − b), so x² − 9 = (x + 3)(x − 3).
- Factoring Trinomials
- FOIL (Multiplying Binomials)
- Multiplying Polynomials Multiplying polynomials means multiplying every term of one by every term of the other, then combining like terms — for example, 2x(3x + 4) = 6x² + 8x.
- Parts of an Algebraic Expression An expression is built from terms separated by + or − signs. Each term has a coefficient (the number) and usually a variable (the letter); a constant is a fixed number. In 7x + 3, 7 is the coefficient, x the variable, 3 the constant.
- Writing Algebraic Expressions Writing an expression means turning a situation into math: “$5 per item for n items” becomes 5n, and adding a $3 fee makes 5n + 3. The variable stands for the amount that can change.
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- Worked examples — Tap the Brain Button on any example for alternative step-by-step explanations.
- Glossary — Plain-English definitions of every key term in the lesson.
- Formula sheet — The GED® & HiSET® formula sheets, on screen while you practice.
- Practice calculator — An on-screen calculator to build your calculator skills before test day.
- Math-fact flashcards — Quick drills for addition, multiplication, perfect squares, and square roots.
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