Polynomial Operations and Factoring

SAT Math · Axiom Academy

Polynomial Operations & Factoring Add, Subtract, Multiply, and Factor Polynomials A polynomial is an expression with one or more terms, each with variables raised to non-negative integer powers. The highest power of the variable. For , the degree is 3. Add/Subtract: Combine like terms Multiply: Use distributive property (FOIL for binomials) Factor: Reverse of multiplication—find the original factors Adding, Subtracting, and Multiplying Polynomials Combine like terms (same variable, same power). Distribute the negative sign to the second polynomial, then combine like terms. Use the distributive property: multiply each term in the first by each term in the second. F irst: multiply first terms of each binomial The SAT loves these patterns. Recognize them instantly to save time. 1. Greatest Common Factor (GCF) Always factor out the GCF first! One of the most common SAT patterns! For polynomials with 4 terms, group them in pairs and factor out common factors. Factor out the common binomial: Grouping usually appears in harder SAT problems. Master this and you'll stand out!

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