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10.5 Factoring x 2 + bx + c

10.5 Factoring x 2 + bx + c. Goal: Factor trinomials of the form x 2 + bx + c Standard: 11.0, 14.0. Standard 11.0.

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10.5 Factoring x 2 + bx + c

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  1. 10.5 Factoring x2 + bx + c Goal: Factor trinomials of the form x2 + bx + c Standard: 11.0, 14.0

  2. Standard 11.0 Students apply basic factoring techniques to second-and simple third-degree polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials. Los estudiantes aplican técnicas básicas de factorización a polinómios de segundo y tercer grado. Estas técnicas incluyen encontrar un factor común para todos los términos del polinómio, reconociendo la diferencia de dos cuadrados, y reconociendo cuadrados perfectos de los binómios.

  3. Standard 14.0 Students solve a quadratic equation by factoring or completing the square. Los estudiantes solucionan una equación cuadrática descomponiendola en factores o completando el cuadrado.

  4. Factor a trinomial • Means to write it as the product of two binomials. • To Factor x2 + bx + c, you need to find numbers p and q such that • P + q = b (linear coefficient) and, • Pq = c (y-intercept)

  5. Conclusion • x2 + bx + c = (x + p)(x + q) • C = pq (multiply) • Find two factors that give you the y-intercept as a result • B = p + q (add or subtract) • Add the previous numbers to find the linear coefficient

  6. Example 1 • Factor x2 + 6x + 8 • A = 1 (leading coefficient, parabola opens upwards) • B = 6 (linear coefficient) • C = 8 (y-intercept when x = 0) • Find two factors that give you your y-intercept or constant 8 • 8 = 1(8), 2(4) multiply • Add the previous numbers to find the linear coefficient 6 • 6 = 2 + 4 • x2 + 6x + 8 = (x + 4)(x + 2)

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