📝 Polynomials and Factoring

Polynomials

A polynomial is a sum of terms with non-negative integer exponents: 3x² + 2x − 7. Terms: monomial (1 term), binomial (2), trinomial (3).

Adding polynomials: combine like terms. Subtracting: distribute the negative, then combine.

Multiplying with FOIL

For (a + b)(c + d): First · First, Outer · Outer, Inner · Inner, Last · Last, then combine like terms.

Example: (x + 3)(x + 5) = x² + 5x + 3x + 15 = x² + 8x + 15.

Factoring Trinomials x² + bx + c

Find two numbers that multiply to c AND add to b. Example: x² + 7x + 12 → find two numbers where product = 12 and sum = 7 → 3 and 4 → (x + 3)(x + 4).