6 – 4: Factoring and Solving Polynomial Equations (Day 1)

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Presentation transcript:

6 – 4: Factoring and Solving Polynomial Equations (Day 1) Objective: Factor polynomial expressions. Use factoring to solve polynomial expressions.

Example 1: Factor the Trinomial A ) 3x3 – 3x2 – 18x GCF = 3x 3x (x2 – x – 6) 3x (x-3)(x+2) B ) 80x4y + 44x3y2 - 16x2y3 GCF = 4x2y 4x2y(20x2 + 11xy – 4y2) 4x2y(5x + 4y)(4x - y)

Special Factoring Patterns: Sum of two cubes 2. Difference of two cubes

Factor each polynomial Example 2: Factor each polynomial x3 + 27 (x + 3) (x2 – 3x + 9) 16u5 – 250u2 GCF: 2u2 2u2(8u3 – 125) 2u2(2u-5)(2u2 + 10 u – 25

For some polynomials you can factor by grouping pairs of terms that have a common monomial factor. The pattern for this is as follows.

Example 4: Factor the polynomial 7x3 – 7x2 + x - 1 (7x3 – 7x2) + (x – 1) 7x2(x – 1) + 1(x – 1) (7x2 + 1)(x – 1) 3x6 – 3x4 + 2x3 – 2x (3x6 – 3x4) + (2x3 – 2x) 3x4(x2 - 1) + 2x(x2 – 1) (3x4 + 2x)(x2 – 1) x(3x3 + 2)(x2 – 1)

HOMEWORK Tomorrow’s Work AM Objectives: #3 Factor Trinomials #4: Factor Sum or Difference of 2 Cubes Tomorrow’s Work AM Objectives: #83 Factor Polynomials into Binomials & Trinomials #84 Factor by Grouping

Example 3: Factor the polynomial

An expression in the form where u is any expression in x is said to be in quadratic form. The factoring techniques for quadratics (factoring, completing the square, and the quadratic formula) can be used to factor such expressions.

Example 3 Factor each polynomial