MATH LESSON FACTORING: QUADRATIC TRINOMIAL When it is not a perfect square, find two numbers that multiply to the last term and add to the middle term! To factor x² + bx + c, find two numbers that multiply to c and add to b. Then write them as (x + p)(x + q). x² + bx + c = (x + p)(x + q) where p × q = c and p + q = b x² + bx + c = (x + p) × (x + q) What is a Quadratic Trinomial? It has 3 terms , the highest degree is 2 , and the leading coefficient is 1 (x²). It is NOT a perfect square trinomial. x² + 5x + 6 — YES, a quadratic trinomial! x² + 6x + 9 — NO, this is a Perfect Square Trinomial! x² − 16 — NO, this is a Difference of Two Squares! The "Factor c, Add to b" Method Look at x² + 5x + 6 . Ignore the x² for now. We need two numbers that: Multiply to c = 6 Add to b = 5 Factors of 6: (1, 6) → 1+6 = 7 ≠ 5 Factors of 6: (2, 3) ...
MATH LESSON FACTORING: PERFECT SQUARE TRINOMIAL A trinomial that is the result of squaring a binomial. Recognize the pattern and factor it in seconds! A Perfect Square Trinomial has exactly 3 terms where the first and last are perfect squares, and the middle term is exactly twice the product of their square roots. a² + 2ab + b² = (a + b)² a² − 2ab + b² = (a − b)² a² + 2ab + b² = (a + b)² a² − 2ab + b² = (a − b)² How to Recognize a Perfect Square Trinomial Check ALL three conditions before factoring: 1. It must be a trinomial (exactly 3 terms) 2. First and last terms must be perfect squares 3. Middle term = 2 × √(first) × √(last) The sign of the middle term tells you which pattern to use: + → (a+b)² | − → (a−b)² The "Double and Multiply" Check This is the most important step ....