6.4: Factoring and Solving Polynomial Equations Objectives: Students will be able to… Factor the sum and difference of 2 cubes Factor by grouping Solve.

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Presentation transcript:

6.4: Factoring and Solving Polynomial Equations Objectives: Students will be able to… Factor the sum and difference of 2 cubes Factor by grouping Solve a polynomial equation by factoring

Complete the table: n n3n3

Factoring Sum and Difference of Cubes: Sum of 2 Cubes: a 3 + b 3 = ( a + b ) (a 2 – ab + b 2 ) EX: x = (x + 4)(x 2 – 4x + 16) Difference of 2 Cubes: a 3 – b 3 = (a –b)(a 2 + ab + b 2 ) EX: (27x 3 – 8) = (3x – 2)(9x 2 + 6x + 4)

Examples: Factor

Factor:

Factor by Grouping Use on some polynomials Group pairs of terms that have a common monomial factor ra + rb + sa + sb = (ra + rb) +(sa + sb) = r (a + b) + s(a +b) = (r +s)(a +b)

Factor:

Solving Polynomial Equations You can use the Zero Product Property to solve higher-degree polynomials. 1.) Set Polynomial equal to 0 2.) Factor Polynomial (We have so many methods to choose from now !!) 3.) Set each factor = 0 and solve.

Find all real number solutions. 2y 5 = 18y

Find all real number solutions 5x x 2 – x – 2= 0

Find all real number solutions. x = 0 Graph the polynomial. What do you notice?

Extra Examples: Find real # solutions.

Find real # solutions, then graph. What do you notice? 4x x 2 = -25

You are building a bin to hold cedar mulch for your garden. The bin will hold 162 ft 3 of mulch. The dimensions of the bin are x ft. high, by 5x -6 ft by 5x -9 ft. How tall is the bin?