# Solving Quadratics: Factoring. What is a factor? Numbers you can multiply to get another number 2  3.

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

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

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

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

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

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

Examples

General Forms

Examples

Difference of two squares

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.

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

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)

Difference of two squares

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