150ch1_3-5

# 150ch1_3-5 - Math 150 Fall 2007 c Benjamin Aurispa 1.3...

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Math 150, Fall 2007, c ± Benjamin Aurispa 1.3 Algebraic Expressions A polynomial is an expression of the form: a n x n + a n - 1 x n - 1 + ... + a 2 x 2 + a 1 x + a 0 The numbers a 1 ,a 2 ,...,a n are called coefcients . Each of the separate parts such as a 3 x 3 or a 1 x is called a term of the polynomial. If there is only one term, it is called a monomial. For two terms, it is called a binomial. For three terms, a trinomial. The degree of the polynomial is n : the highest power of x . To add (or subtract) polynomials, we combine like terms (those that have the same variables raised to the same powers). Example: Find the di±erence ( x 3 - 4 x 2 + 6 x + 12) - (2 x 3 + x 2 - 4 x - 6) To multiply polynomials, we use the distributive laws. In particular, to multiply two binomials, we use the FOIL method. Examples Multiply ( x - 7)(2 x + 3) Multiply ( x - x + 5)( - 3 + 4 x ) Special Product and Factoring Formulas 1. ( A + B )( A - B ) = A 2 - B 2 2. (a) ( A + B ) 2 = A 2 + 2 AB + B 2 (b) ( A - B ) 2 = A 2 - 2 AB + B 2 3. (a) ( A + B ) 3 = A 3 + 3 A 2 B + 3 AB 2 + B 3 (b) ( A - B ) 3 = A 3 - 3 A 2 B + 3 AB 2 - B 3 4. (a) ( A + B )( A 2 - AB + B 2 ) = A 3 + B 3 (b) ( A - B )( A 2 + AB + B 2 ) = A 3 - B 3 Going toward the right in these formulas is expanding. Going toward the left is factoring. 1

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± Benjamin Aurispa Examples : Expand the following. (2 x + 3)(2 x - 3) ( x 3 - 4) 2 ( x 2 - 2) 3 Factoring Steps 1. Factor out all common factors. 2. See if you can use a special factoring formula. 3. See if you can factor by grouping. 4. Use trial and error. Examples
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## This note was uploaded on 10/08/2009 for the course MATH 150 taught by Professor Unknown during the Fall '08 term at Texas A&M.

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150ch1_3-5 - Math 150 Fall 2007 c Benjamin Aurispa 1.3...

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