Transcripción 10/3/2026, 12:04:24 p. m.

Apuntes

• Factoring Quadratic Expressions: Basic and Advanced We start with the quadratic expression: 2P² + 3P - 5 This can be factored as: (2P + 5)(2P - 1) Dividing by 2: (2P + 5)²(P - 1) which simplifies to: (2P + 5)(P - 1) --- • Divisors of Numbers D(12) = ±1, ±2, ±3, ±4, ±6, ±12 D(10) = ±1, ±2, ±5, ±10 --- • Continuing Factoring: Case 3 – Trinomials a) Quadratic trinomial with leading coefficient 1: x² + bx + c b) Quadratic trinomial with leading coefficient a ≠ 1: ax² + bx + c --- • Examples of Factoring Trinomials 1) x² + 5x + 6 Factorization: (x + 2)(x + 3) 2) t³ - 3t² - 4t Factor out t: t(t² - 3t - 4) Factor the quadratic: t(t - 4)(t + 1) 3) K² + 5K + 6 Factorization: (K + 2)(K + 3) --- • Factoring More Complex Trinomials 2) t³ - 3t² - 10t Factor out t: t(t² + 3t - 10) Factor the quadratic: t(t - 5)(t + 2) 3) K² + 5K t - 14t² First, ignore t: K² + 5K - 14 Factor as: (K + 7)(K - 2) Now, reintroduce t: (K + 7)(K - 2t) --- • Factoring with Leading Coefficient Not Equal to 1 b) For the quadratic expression: 4) 3m² + 11m - 4 Solution: Factor as: (3m + 12)(3m - 1) Divide by 3: (3m + 4)(3m - 1) --- This completes...