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Sec-42 - Math 1300 Section 4.2 Notes Special Polynomials...

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Math 1300 Section 4.2 Notes 1 Special Polynomials Patterns Certain polynomials can be factored by finding a pattern. This section deals with four special patterns for factoring polynomials: difference of squares, difference of cubes, sum of cubes, and perfect square trinomials. Difference of Squares The difference of squares pattern can be identified by looking at the polynomial. It must be a binomial, the first term must be a variable to the second power (a.k.a. squared) and a constant term must be subtracted from it. There is no first-order variable term in a difference-of-squares polynomial. The formula ) )( ( 2 2 b a b a b a + - = - is how a difference of squares polynomial is factored. Example: Factor x 2 – 25. This binomial has its first term is x 2 , a second-order monomial. The only other term is 25, just a constant. This means x 2 – 25 can be factored using the difference of squares pattern, so x 2 – 25 = ( x ) 2 – (5) 2 = ( x – 5)( x + 5). To check, we can multiply the factored form back together using the FOIL method: ( x – 5)( x + 5) = x 2 + 5 x – 5 x – 25 = x 2 – 25.
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