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10.8 Factoring Cubic Polynomials

10.8 Factoring Cubic Polynomials. Goal: Factor cubic polynomials Standard: 11.0. Standard 11.0.

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10.8 Factoring Cubic Polynomials

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  1. 10.8 Factoring Cubic Polynomials Goal: Factor cubic polynomials Standard: 11.0

  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. A Polynomial is prime if it cannot be factored using integer coefficients.To factor a polynomial completely, write it as a product of a monomial and prime polynomials.

  4. Graphic Calculator • Y-intercept -16 when x = 0 • (3x+4)=0, then x=-4/3 • It is the 1st. solution • (3x-4)=0, then x=4/3 • It is the 2nd. solution

  5. Example 1 • Finding the Greatest Common Factor • Factor the greatest common factor out of 8x4 - 24x2 • Solution • Write each term using prime factors. • 8x4= 23(x4) 24x2 = 23(3)(x2) • 23x2 is the greatest common factor. • Use the distribute property to factor out the greatest common factor from each term. • 8x4 - 24x2 = 8x2 (x2-3)

  6. Example 2 - Factor Completely • Factor 8x2 - 32 completely. • Solution • 8x2 - 32 = 8(x2-4) Factor out the greatest common factor, 8. • =8(x - 2) (x + 2) Factor the difference of two squares.

  7. Example 4- Factoring the Sum of Difference of two Cubes • Factor: a. x3 +8 b.a3 - 64. • Solution • A.x3 + 8=x3 + 23 Write as a sum of two cubes. • =(x+2) (x2-2x + 4) Use special product pattern. • B.a3 - 64= a3-43 Write as a difference of two cubes. • =(a-4)(a2 + 4a + 16) Use special product pattern.

  8. Example 3- Factoring by Grouping • Factor x3 + 4x2 - 9x - 36 completely. • Solution • X3 + 4x2 - 9x - 36 =(x3+4x2) + (-9x-36)Group terms • =X2(X=4) - 9(X+4)Factor each group • =(X2-9)(X=4)Use distributive property. • =(X=3)(X-3)(X=4)Factor difference of two squares.

  9. Graphic Calculator • Y-intercept -25 when x = 0 • (x+5)=0, then x=-5 • It is the 1st. solution • (x-5)=0, then x=5 • It is the 2nd. solution

  10. Perfect Square Trinomial Pattern • Take square root of each term and square the whole binomial

  11. Graphic Calculator • Y-intercept 16 when x = 0

  12. Perfect Square Trinomial Pattern • Take square root of each term and square the whole binomial

  13. Graphic Calculator • Y-intercept 36 when x = 0

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