Download 5.4 Factoring with GCF

Warm-up
Find the GCF for the following.
1. 10, 25
2. 12, 16, 24
3. 8xy, 12x
Divide the following
35
xy
4.
7x
5. 75 x
6
15 x
3
24 x3 y 4
6.
6 x3 y 2
Foundations of Algebra
UNIT QUESTION: In what ways can
algebraic methods be used in
problems solving?
Standard: MM1A2
Today’s Question:
How do we find the GCF of a
polynomial?
Standard: MM1A2f
What is the greatest common factor??
6
4
2
-4x -x -2x
2
-x
Note: With negatives, go by the leading term!!
FACTORING POLYNOMIALS
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.
Example 1
4x + 6y
What is the GCF?
2
Factor out the GCF:
4x 6 y

2
2
2(2x + 3y)
Example 2
6x3 – 9x2 + 12x
What is the GCF?
3x
Factor out the GCF:
6 x3 9 x 2 12 x


3x 3x 3x
3x(2x2 – 3x + 4)
Factor
2
3. 16x – 8x
= 8x(2x – 1 )
4. 2a3 – 6a
= 2a(
2
a
–3 )
What is their
GCF?
Factor
2
5. 2x y + 2x
= 2x( xy + 1)
6. 6xy + 9y2
= 3y(2x + 3y )
What is their
GCF?
Homework/Classwork
GCF Factoring WS