1.3 Algebraic Expressions
Expand, factor, and simplify polynomials.
Before you solve
Ideas in this lesson
Review the ideas below. Select one to see worked steps and five practice questions.
01Polynomials: vocabulary, degree, addition and subtractionWorked steps · five questions02Multiplying polynomialsWorked steps · five questions03Special product formulasWorked steps · five questions04Factoring out a common factorWorked steps · five questions05Factoring trinomialsWorked steps · five questions06Special factoring formulasWorked steps · five questions07Factoring by groupingWorked steps · five questions08Factoring completely, including fractional exponentsWorked steps · five questions09Recognize deeper factor structure and prove identitiesWorked steps · five questions10Explain polynomial identities, degree and geometryWorked steps · five questions
Lesson brief and rules
1.3 Algebraic Expressions
Distribute multiplication across every term. To factor , find two numbers with sum and product .
Remember
Check a factorization by multiplying back.
Check a factorization by multiplying back.
Worked example
01 / For , identify the degree and leading coefficient.
02 / The expression is already ordered by descending powers.
03 / The greatest exponent is , so the degree is .
04 / The coefficient multiplying that highest power is .
Worked example 2 · Polynomials: vocabulary, degree, addition and subtraction
Add .
Group the quadratic terms, linear terms, and constants separately.
The coefficients become , , and .
Combine only those like terms to obtain .
Textbook reference: Stewart, Redlin & Watson, Precalculus: Mathematics for Calculus, 7th ed. (Cengage, 2016). The explanations and practice here are original, organized by textbook section.