Objectives:

1
5-4 Factoring Quadratic Expressions

• Objectives
• --To find common and binomial factors of
  quadratic expressions
• -- To factor special quadratic expressions

2
DEFINITIONS

• Factoring rewriting an expression as the product
  of its factors
• GCF greatest common factor common factor of
  the terms of the expression. Its the common
  factor with the greatest coefficient and the
  greatest exponent. You can factor any expression
  that has a GCF not equal to 1.
• Perfect Square Trinomial the product you obtain
  when you square a binomial.
• Difference of Two Squares an expression of the
  form

3
Finding Common Factors

• Factor each expression.
• Factor
  out the GCF, 4this gives
• then
  rewrite using the distributive property
• This is
  factored form.
• Factor
  out the GCF, 3n..this gives
• then
  rewrite using the distributive property
• This is
  factored form.
• Factor the following expressions
• a) b)
  c)

4
Factoring using ac method

• A quadratic trinomial is an expression in the
  form
• To factor
• Multiply a times c
• Find factors of that product that add up to b
• Use those factors to rewrite the quadratic into
  a polynomial with 4 terms
• Group first two terms together and group last two
  terms together, leaving the sign of the 3rd term
  between the parentheses
• Factor out the GCF from both groups
• Rewrite as the product of two binomials.

5
Keep the following in mind

• If ac and b are positive, then the factors of ac
  are both positive
• If ac is positive and b is negative, then the
  factors of ac are both negative
• If ac is negative, then the factors of ac have
  different signs
• If ac is positive, then the factors of ac have
  the same sign

6
Factor the following

• a)
  b)
• c)
  d)
• e)
  f)
• g)
  h)
• i)
  j)

7
Factoring Special Expressions

• Factoring Perfect Square Trinomials
• Factoring a Difference of Two Squares

8
Factor the following

• a) Rewrite the first
  and third terms as squares to get
• Rewrite the middle term to verify the perfect
  square trinomial pattern to
• get
  
• Rewrite as a binomial squared
  
• a)
  b)
• c)
  d)