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Common Factoring

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

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Common Factoring

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  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)

  3. Exponent Laws

  4. Radicals!

  5. 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

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

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

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

  9. Radicals and Exponents 68 65 = = = 63

  10. 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

  11. 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)

  12. Radicals and Exponents = x x = =

  13. 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

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

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