Transcript Factoring using GCF

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