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Published byKelly Holt Modified over 6 years ago

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

Objective: Factor polynomial expressions. Use factoring to solve polynomial expressions.

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**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)

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**Special Factoring Patterns: Sum of two cubes**

2. Difference of two cubes

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**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)(2u u – 25

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

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**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)

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**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

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**Example 3: Factor the polynomial**

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**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.

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Example 3 Factor each polynomial

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