5.4 Factoring Polynomials

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1Methods

Examples

Practice Problems

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Definition

If a polynomial is a product of other polynomials, then each polynomial in the product is a factor

Factors that contain polynomials of a positive degree are called nontrivial factors

Polynomials than cannot be factored are referred to as prime or irreducible

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Greatest Common Factor (GCF) Look for the largest common number

and/or variables in each term Divide each term by the common terms

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Grouping

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Rainbow Method (2nd degree Polynomial)

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Simplifying Quotients

Factor the numerator Factor the denominator Cancel any like polynomials

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Special Cases

Factoring Formulas Example

Difference of two Squares:x2 – y2 = (x + y)(x - y)

9a2 – 16=(3a)2 – (4)2

= (3a + 4)(3a – 4)

Difference of two Cubes:x3 – y3 = (x - y)(x2 + xy +

y2)

8a3 – 27= (2a)3 – (3)3

= (2a – 3)[(2a)2 + (2a)(3) + (3)2]

=(2a – 3)(4a2 + 6a + 9)

Sum of two Cubes:x3 + y3 = (x + y)(x2 – xy +

y2)

125a3 + 1= (5a)3 + (1)3

= (5a + 1)[(5a)2 – (5a)(1) + (1)2]

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Practice Problems

Page 242Problems 5-11, odd

15-37, odd46-51