1. 4.4 FACTORING QUADRATIC
EXPRESSIONS
Part 1

2. FACTORS
 Factors are the numbers you multiply together
to get another number.
 The factors of an expression are expressions
that you multiply together to get another
expression.
 Factoring is rewriting an expression as a
product of its factors.

3. FACTORING
 To factor a polynomial means to transform it
to a product of two or more factors (usually
binomials)
 Factoring is the reverse process of FOIL (Double
Distribution)
 FOIL can be used to check your work

4. TO FACTOR A POLYNOMIAL
OF THE FORM
1. What are factors of c that add up to b?
2. Set up factors
3. Plug in the numbers
4. Check
2
x bx c± +
( ) ( )x x

5. FACTOR EACH EXPRESSION
2
9 20x x+ +

6. FACTOR EACH EXPRESSION
2
14 72x x+ −

7. REMEMBER
 When the third term is positive in a quadratic
trinomial, the binomial factors have the same sign

8. THIRD TERM IS NEGATIVE
 When the third term is negative the binomial
factors have opposite signs
( ) ( )2
x bx c x x± − = + −

9. GCF
 The greatest common factor (GCF) of an
expression is a factor that all the terms in an
expression have in common.
 Always factor out the GCF first!
 The GCF can be a number, a variable, or both

10. FIND THE GCF OF THE
EXPRESSION. THE FACTOR
THE EXPRESSION.
2
7 21n −

11. FIND THE GCF OF THE
EXPRESSION. THE FACTOR
THE EXPRESSION.
2
6 9x x+

12. FIND THE GCF OF THE
EXPRESSION. THE FACTOR
THE EXPRESSION.
2
4 20 56x x+ −

13. FIND THE GCF OF THE
EXPRESSION. THE FACTOR
THE EXPRESSION.
2
9 9 18x x+ −

14. FACTOR EACH EXPRESSION
2
13 12x x− + −

15. LEADING COEFFICIENTS
 The leading coefficient of a polynomial is the
coefficient of the term with the highest degree
 We know how to factor quadratic trinomials
whose leading coefficient is 1
 We will learn how to factor quadratic trinomials
whose leading coefficients are not 1

16. THE ARC METHOD
 Used to factor quadratic trinomials whose
leading coefficients are not 1

17. STEPS OF THE ARC METHOD
1. “Arc” the leading coefficient
2. Factor
3. Divide both by the leading coefficient that was
arced
4. Simplify if possible
5. Undo the arc
6. Check

18. FACTOR THE EXPRESSION
2
2 11 12x x+ +

19. FACTOR THE EXPRESSION
2
4 4 3x x− −

20. FACTOR THE EXPRESSION
2
2 7 6x x− +

21. HOMEWORK
 P221 #1 – 3, 15 – 45odd