Polynomials Functions

SAT Math — Polynomials and Function Notation ## Polynomial Basics A polynomial is an expression with multiple terms, where the variables have whole-number exponents. You've already seen linear (degree 1) and quadratic (degree 2) polynomials. The SAT also tests higher-degree polynomials. Key vocabulary: - Degree: The highest exponent in the polynomial (e.g., x³ + 2x² − x + 5 is degree 3) - Leading coefficient: The coefficient of the highest-degree term - Constant term: The term with no variable ## Polynomial Operations Adding/Subtracting: Combine like terms (same variable, same exponent) > (3x² + 5x − 2) + (x² − 3x + 7) = 4x² + 2x + 5 Multiplying: Use the distributive property; multiply every term in one by every term in the other. > (x + 3)(x² − 2x + 1) > = x(x² − 2x + 1) + 3(x² − 2x + 1) > = x³ − 2x² + x + 3x² − 6x + 3 > = x³ + x² − 5x + 3 FOIL (for two binomials): First, Outer, Inner, Last > (x + 4)(x − 2) = x² − 2x + 4x − 8 = x² + 2x − 8 ## Function Notation: f(x) f(x) (read "f of x") means a function named f with input x. Evaluating a function: Substitute the input value wherever you see x. > f(x) = 2x² + 3x − 1 > f(4) = 2(4)² + 3(4) − 1 = 32 + 12 − 1 = 43 f(a + b): Replace every x with (a + b): > f(x) = x + 5 > f(a + b) = (a + b) + 5 = a + b + 5…