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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!)
Example 2: Factor.
a)
b)
c)
2x2 8x
9x2 y 3xy2
12m3n2 6m4n3 4m2n5 2m2n2
Exponent Laws
Radicals!
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 34 is the power
3 is the base
4 is the exponent
Radicals and Exponents
53 = “5 to the three”
64 = “six to the four”
Hizzo = “H to the Izzo”
Radicals and Exponents
63 = 6 x 6 x 6
Radicals and Exponents
52 x 55
= (5 x 5) x (5 x 5 x 5 x 5 x 5)
= 57
Radicals and Exponents
68 65
=
=
= 63
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
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)
Radicals and Exponents
= x x
=
=
• 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
The Power of Negative Numbers
Homework
p. 399 # 1 – 3, 5 – 11 (alternating!)
Challenge
Pg. 401 #16 – 18