Polynomial Expressions
Lessons in this chapter
About Polynomial Expressions
Polynomial Expressions builds the vocabulary and operations for polynomials, expressions with multiple terms involving powers of a variable.
Introduction to Algebraic Expressions and Properties of Algebraic Expressions review expression vocabulary and properties from middle school, before Introduction to Polynomial Expressions names a polynomial by its number of terms and its degree (the highest power present).
Addition, Subtraction and Multiplication of Polynomials covers combining polynomials using each operation, while Special Products of Polynomial Expressions covers shortcut patterns, like (a + b)²: that come up often enough to memorize directly rather than multiplying out every time.
Modeling with Polynomial Expressions closes the chapter by writing a polynomial expression to represent a real situation, like the area of a shape with algebraic side lengths.
All six lessons in this chapter open as Algebra 1 worksheets in the page, including Properties of Algebraic Expressions, Addition, Subtraction and Multiplication of Polynomials and Special Products of Polynomial Expressions. Each question is marked as you answer it, so an unlike term combined by mistake is caught on that question rather than carried through the rest of the algebra practice. The worksheets are free to try, with no login needed for your first 3.
Frequently asked questions
Introduction to Algebraic Expressions and Properties of Algebraic Expressions revisit the expression work most students first meet in pre algebra: terms, coefficients, like terms and the distributive property. Introduction to Polynomial Expressions then names degree and standard form, Addition, Subtraction and Multiplication of Polynomials combines them, and Special Products of Polynomial Expressions covers the square of a binomial and the difference of two squares as patterns worth recognizing. Modeling with Polynomial Expressions closes by writing a real quantity, such as an area, as a polynomial. The chapter sits in the high school Algebra conceptual category (A).
A polynomial is an expression made of terms with non-negative whole-number exponents on its variables, classified by its number of terms (monomial, binomial, trinomial) and its degree (the highest exponent present).
Combine like terms: terms with the exact same variable part raised to the exact same power, the same rule used for combining like terms in any algebraic expression.
Multiply every term in the first polynomial by every term in the second, using the distributive property repeatedly, then combine any resulting like terms.
Special products are common multiplication patterns, like (a + b)² = a² + 2ab + b², or (a + b)(a - b) = a² - b²: that come up often enough to recognize and apply directly, saving the work of multiplying everything out term by term.
Forgetting one of the four multiplications required (often remembered as FOIL: First, Outer, Inner, Last), skipping the "outer" or "inner" product is the single most common way to get an incomplete answer.