Why this chapter matters
Factoring reveals zeros and structure that are hidden in expanded form, making later equation solving and graph analysis possible.
What you will learn
- Classify polynomials by degree and number of terms.
- Add and multiply polynomials accurately.
- Factor greatest common factors, trinomials, and differences of squares.
Lessons in this chapter
- Polynomial operationsCombine and multiply polynomial terms without mixing degrees.
- Greatest common factorsRemove the largest shared factor before using other patterns.
- Factoring trinomialsReverse multiplication to express a quadratic as two binomials. Read the full guide →
- Special productsRecognize perfect squares and differences of squares.
Study task
Build and simplify an expression for the area of a rectangular garden with sides x + 3 and x + 5, then factor the expanded result back.
Chapter checkpoint
Factor x^2 + 7x + 12.
Find two numbers that multiply to 12 and add to 7: 3 and 4. The factorization is (x + 3)(x + 4).