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Factoring using GCF Algebra I Definitions • Prime number – is a whole number whose only • • • factors are itself and one (a number can’t be factored any more) Composite number – is an integer that can be factored Greatest Common Factor – of two monomials is the product of their common factors (largest number that will go into 2 numbers) Factored Form – A monomial is in factored form when it is expressed as the product of prime numbers and variables and NO variable has an exponent greater than 1. Factor any problem into prime factors first 180 = 2 2 3 3 5 • 1) Factor 180 90 2 45 2 Now list out All the Prime factors List them in numerical order 9 5 3 3 2) Find the GCF of 54, 63, 180 • 54 = 2 3 3 3 3 3 7 • 63 = • 180 = 2 2 3 3 5 • The GCF is Which factors do each of these have in common? 3 3 =9 •Greatest Common Factor – of two monomials is the product of their common factors (largest number that will go into 2 numbers) 3) Find the GCF of 24, 64, 80 • 24 = 2 2 2 3 Which factors • 64 = 2 2 2 2 2 2 do each of these • 80 = 2 2 2 2 5 have in common? • The GCF is 2 2 2=8 •Greatest Common Factor – of two monomials is the product of their common factors (largest number that will go into 2 numbers) 4) Factor GCF of 10y2 + 15y • 10y2 =2 5 y y • 15y = 3 5 y 5 y = 5y Which factors do each of these have in common? 10 y 15 y 2 Use distributive property 5y (2 y 3) 5) Factor GCF of 21ab – 33a2bc • 21ab =3 7 a b • 33a2bc = 3 11 a a b c 3 a b = 3ab 21ab 33a bc 2 Use distributive property 3ab (7 11ac) 6) Factor GCF of 4x3 – 12x2 +20x • 4x3 = 2 2 x x x • 12x2 = 2 2 3 x x • 20x = 2 2 5 x 2 2 x = 4x 4 x 12 x 20 x 4x ( x 2 ) 4x (3 x ) + 4x (5) 3 2 4x( x 3x 5) 2 Use distributive property 7) Factor GCF of 2x3 + 4x2 + 6x • 2x3 = 2 x x x • 4x2 = 2 2 x x 2 3 x • 6x = 2 x = 2x 2x 4x 6x 3 2 2x ( x 2 ) 2x (2 x) + 2x (3) 2x( x 2 x 3) 2 Use distributive property