Chapter 6 Notes-  Exponents and Polynomials

1.  Product and Quotient rules for exponents

    aⁿ.a^m  = a^{n + m};  Example   a².a³  = a⁵ (2factors of a and 3 factors of a make a total of 5 factor)

     aⁿ/a^m = a^{n - m};  Example   a⁵/a³  = a² ( three factors in the denominator will cancel three in the numerator  leaving a net of  2 factors)            

    Other rules that you should know and be able to work with  

                        (a^m)ⁿ  = a^mn

                         (ab)^m = a^m.b^m

                         (a/b)^m = a^m/b^m

                               a⁰ = 1 ( a not equal to 0); because a/a = 1

                          a^-n = 1/aⁿ ( a not equal to 0); because 1 = a⁰ and 1/aⁿ = a⁰/aⁿ = a^-n

2. Addition and subtraction of polynomials- basically it is to combine like terms

3. Products of binomials-    FOIL method  - Example (x + 2) (x + 1) = x2 +3x +2; product of First terms x2, Outer terms 1x, Inner terms 2x, product of last terms 2.

Special formulas- (a + b)² = a² + 2ab + b²

                                     (a - b)² = a² - 2ab + b²

4. Quotient of two polynomials-  Division problem