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Published bySusan Tate Modified over 5 years ago

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Solving Quadratics: Factoring

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What is a factor? Numbers you can multiply to get another number 2 3

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Factoring Polynomials This process is basically the REVERSE of the distributive property. distributive property factoring Factored formStandard form

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In factoring you start with a polynomial and you want to rewrite it as a product. Factoring Polynomials Three terms Factored form

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Techniques of Factoring Polynomials 1. Always look for the Greatest Common Factor (GCF) first.

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Standard Form of Quadratic Equations

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2. Factoring Trinomials. Is there a GCF? Techniques of Factoring Polynomials New Method: product of two binomials (x+ )(x+ )

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2. Factoring Trinomials. We need to find factors of a c ….that add up to b Techniques of Factoring Polynomials

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Examples

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General Forms

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Examples

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Difference of two squares

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Note… Not every quadratic expression can be factored into two factors. For example x 2 – 7x + 13. We may easily see that there are no factors of 13 that added up give us –7 x 2 – 7x + 13 is a prime trinomial.

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Your Turn!

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Factoring the Difference of Two Squares The difference of two bases being squared, factors as the product of the sum and difference of the bases that are being squared. a 2 – b 2 = (a + b)(a – b) FORMULA: (a + b)(a – b) = a 2 – ab + ab – b 2 = a 2 – b 2

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Factoring the difference of two squares Factor x 2 – 4y 2 Factor 16r 2 – 25 (x) 2 (2y) 2 (x – 2y)(x + 2y) Now you can check the results… (4r) 2 (5) 2 Difference of two squares Difference Of two squares (4r – 5)(4r + 5) a 2 – b 2 = (a + b)(a – b)

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Difference of two squares

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