1. Common Factoring • When factoring polynomial expressions, look at both the numerical coefficients and the variables to find the greatest common factor (G.C.F.) • Look for the greatest common numerical factor and the variable with the highest degree of the variable common to each term • To check that you have factored correctly, EXPAND your answer (because EXPANDING is the opposite of FACTORING!)

2. Example 2: Factor. a) b) c)

4. Exponent Laws

5. Radicals!

6. Radicals and Exponents • A radical is a root to any degree E.g. is a squared root, is a cubed root. • A repeated multiplication of equal factors (the same number) can b expressed as a power Example: 3 x 3 x 3 x 3 = 34 34is the power  3 is the base  4 is the exponent

7. Radicals and Exponents 53 = “5 to the three” 64 = “six to the four” Hizzo = “H to the Izzo”

8. Radicals and Exponents 63 = 6 x 6 x 6

9. Radicals and Exponents 52 x 55 = (5 x 5) x (5 x 5 x 5 x 5 x 5) = 57

10. Radicals and Exponents 68 65 = = = 63

11. Radicals and Exponents = (72) x (72) x (72) = (7 x 7) x ( 7 x 7) x (7 x 7) = (7 x 7) x ( 7 x 7) x (7 x 7) = 76

12. Radicals and Exponents = (3 x 2) x ( 3 x 2) x (3 x 2) x (3 x 2) = (3 x 3 x 3 x 3) x (2 x 2 x 2 x 2) = (34) x (24)

13. Radicals and Exponents = x x = =

14. The Power of Negative Numbers • There is a difference between –32 and (–3)2 • The exponent affects ONLY the number it touches So, –32= –(3 x 3), but (–3)2 = (–3) x (–3) = –9 = 9

15. Homework p. 399 # 1 – 3, 5 – 11 (alternating!) Challenge Pg. 401 #16 – 18