Transcript Slide 1

```6.1
Factoring Polynomials
Standard 11.0: Find a
common factor to all of the
terms in a polynomial
Vocabulary
1. Monomial
2. Polynomial
1. One Term
2. A monomial or sum of
monomials
3. Removing common
3. Factor
factors from each term
of a polynomial
4. Greatest Common 4. The largest factor that
Factor (GCF)
occurs in each term.
#1 Factor
x  3x
x x
2
Divide by the GCF
GCF:
x(x  3)
Check
x(x  3)  x  3x
2
x
#2 Factor
a b  2ab
ab ab
2
Divide by the GCF:
GCF:
ab(a  2)
Check
ab(a  2)  a b  2ab
2
ab
#3 Factor
3x  5 x  2 x
2
2
2
x
x
x
6
Divide by the GCF:
3
2
GCF:
x
2
x (3x  5 x  2)
2
4
Check
x (3x  5x  2)  3x  5x  2 x
2
4
6
3
2
#4 Factor
2 p q  p q  pq GCF: pq
pq
pq pq
3 2
Divide by the GCF:
2
pq(2 p q  p  1)
2
Check
pq(2 p q  p  1)  2 p q  p q  pq
2
3
2
2
#5 Factor
12m n  3m n  6m n
2 2
2 2
2 2
3m n
3m n 3m n
4
4
3 3
2
2
GCF:
3m n
3m n (4m n  mn 2)
2 2
2
2
Check
3m n (4m n  mn 2) 
2 2
2 2
12m n  3m n  6m n
4
4
3 3
2
2
2
2
Vocabulary
5. Relatively Prime 5. Polynomials that have
no common factors.
#6 Are the following relatively prime?
3a  a,
2
a  2a
3
What is the largest factor common to both
polynomials?
3a  a,
a
2
a  2a
a
3
No
```