Factors
When two numbers are multiplied, each number is
called a factor of the product.
List the factors of 18:
18: 1, 2, 3, 6, 9, 18
* Calculators: Y = (the number) / x
2nd Graph
Prime and Composite Numbers
Prime Number – a whole number greater
than 1 that’s only factors are 1 and itself.
Composite Number – a whole number
greater than 1 that has more than two
factors.
Greatest Common Factor
Greatest Common Factor (GCF) – the
greatest number or monomial that is a factor of
ALL of the original terms.
Steps:
1. Look at the factors of the smallest coefficient.
2. The GCF is the largest factor that goes into
ALL of the other coefficients.
3. For each variable that ALL of the terms have,
the GCF is always the smallest exponent.
Finding the GCF
Find the GCF of each set of monomials.
1) 12, 42
2) 48, 60
For variables that ALL terms have in
common, the GCF is always the smallest
exponent that you have of each variable.
3) x3, x5
4) z4, z2
5) 12a5, 18a2
6) 18xy, 36y2
7) 36x2y, 54 xy2z
8) 12a5c7, 24a3b2c, 18a10b4c3
Factoring
To factor an expression means to break it up into
two or more things that multiply to the original
expression.
Factoring Using the GCF
Factoring with a GCF is basically the
opposite of using the distributive property.
4a (3a + 4)
2
12a
+ 16a
Factoring Using the GCF
Steps:
1) Find the GCF of ALL of the terms. The
GCF will be on the outside of the ( ).
2) Divide each original term by the GCF to
get each term inside the ( ).
* You always have to have the same number of
terms inside the ( ) as you started with.
9) Factor
25a2 + 15a
10) Factor
18x2 – 12x3
11) Factor
28a2b + 56abc2
12) Factor 28a2 + 21b – 35b2c2
13)
Factor
3x2y – 27x5y3z + 18x3y7z2
14) Factor
1.
2.
3.
4.
2
16xy
2y2(8x – 12z + 20)
4y2(4x – 6z + 10)
8y2(2x - 3z + 5)
8xy2z(2 – 3 + 5)
-
2
24y z
+
2
40y
15) Factor
1.
2.
3.
4.
x(20 – 24y)
2x(10x – 12y)
4(5x2 – 6xy)
4x(5x – 6y)
2
20x
– 24xy
Homework
Worksheet pg. 529 #’s 1 – 12