mac1140_lecture3_2 - L3 1.4 Factoring Factoring out a 1 Factoring the process of finding polynomials whose product is equal to a given polynomial

mac1140_lecture3_2 - L3 1.4 Factoring Factoring out a 1...

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20 L3 §1.4 Factoring Factoring – the process of finding polynomials whose product is equal to a given polynomial. A polynomial is considered to be factored completely if it is written as a product of prime or irreducible polynomials. Factoring out the GCF ( Greatest Common Factor ): Use the distributive property to factor out the GCF. The GCF is the product of the largest common factor of all numbers and all common factors containing variables, each with the smallest exponent that appears on that factor. Example . Factor out the GCF from each polynomial: a) 5 3 9 8 6 x y xy + b) 2 3 2 5 ( 2) ( 2) x x x x + 21 Factoring out a 1 : Example . Use the distributive property to simplify: 2 (2 3 4) x x + = By using the distributive property, we can factor a 1 out of a polynomial by changing the sign of each term. Example. Factor a 1 out of each polynomial: a) 2 x b) 2 3 4 5 x x + Factoring by grouping: Sometimes this method works when we have a polynomial with more than 3 terms. To apply, collect

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