Download Notes – Greatest Common Factor (GCF)

CCGPS Adv Algebra
Unit 1A – Polynomials
1A.6 – Notes
Name: __________________________________________ Date: _____________________________
Greatest Common Factor (GCF)
GCF with Variables
 With variables, the GCF will always be the ___________ exponent of a common
variable.
 Examples: Find the GCF:
1. 12 x 3 , 16 x 2
2. 45 a 5 , 50a 7
3. 5 a, 35
4. 3 y , -8xy
5. 22 x 2 , -11x
6.
4x
6
x
4
2x
2
Factoring Polynomials Using GCF
 Factoring: Write the polynomial as a product.
Steps:
1. Find the GCF of all its terms.
2. Write the polynomial as a product by factoring out the GCF from all the terms.
- This is done by dividing the original terms of the polynomial by the GCF.
3. The remaining factors in each term will form a polynomial.
Examples:
4x
6y
6x
3
9x
2
12 x
Practice Problems:
1. 16 x 2
8x
3. 2 h2 k 2 k
2. 2 a 3
6a
4. 6uv 9 v 2
CCGPS Adv Algebra
Unit 1A – Polynomials
1A.6 – Notes
Factoring Trinomials
***Always check for a ___________ first!!***
Trinomials
ax
2
bx
c, a
1
 What _______________ to give you the first term?
 What _______________ to give you the last term, but ________________ to give
you the middle term?
1. +c, ________________ signs
2. – c, ________________ signs
Examples: Factor the following trinomials:
x
2
9x
14
Factoring Trinomials:
2x
2
11x
You Try!
1. x 2 12 x
9
32
x
ax
2
bx
c, a
2
x
20
x
2
5x
14
1
6x
2
33 x
15
4x
2. 2 x 2 10 x 12
3. 3 x 2
2
4x
2x
3
5
CCGPS Adv Algebra
Unit 1A – Polynomials
1A.6 – Notes