1300_F2011_Sec_42-filled

1300_F2011_Sec_42-filled - Math 1300 Section 4.2 Special...

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Math 1300 Section 4.2 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 1: Factor x 2 – 25. Example 2: Factor 9 x 2 – 49. Example 3: 2 4 100 x - Note: There is no sum of squares factorization; that is, we can’t factor a 2 + b 2 . Difference of Cubes To find the pattern for the difference of cubes, the polynomial to factor must be a binomial, the first term must be a variable to the third power (a.k.a. cubed) and a constant term must be
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1300_F2011_Sec_42-filled - Math 1300 Section 4.2 Special...

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