Factoring Quadratics: Perfect Square Trinomial

1
Factoring QuadraticsPerfect Square Trinomial
2
A Perfect Square Trinomial is a trinomial in
the form (p)22(p)(q)(q) 2 . Note the first
and last terms are perfect squares and the middle
term is twice the product of these perfect square
bases. The trinomial below fits this form.

3

• is a Simple
  Trinomial It can be factored as follows,

This gives the rule for factoring a Perfect
Square Trinomial
To review Simple Trinomial Factoring, search
the OERB for Factoring Quadratics-Simple
Trinomials
4

• Factor using the rule
  in the previous slide

Recall

5

• This gives

Note If the rule for factoring a Perfect Square
Trinomial is forgotten, then it can be factored
as a Simple Trinomial or a Difficult Trinomial.
6

• This gives the same result, as seen below, for
  the Difficult Trinomial from the previous slide
  

AUSTRALIAN METHOD
METHOD OF DECOMPOSITION

To review Difficult Trinomial Factoring, search
the OERB for Factoring Quadratics-Difficult
Trinomials AUSTRALIAN METHOD or Factoring
Quadratics-Difficult Trinomials Method of
DECOMPOSITION.
7

• Factor .

8

• Solution

(1)Check it is a Perfect Square Trinomial.
9

• Solution

(2) Factor using the Perfect Square Trinomial
rule.
10

• Solution

Here pk and q8, for the rule (p)22(p)(q)(q)
2(p q) 2 .
11

• Alternate Solution Use the Simple Trinomial
  factoring method.

12

• Reminder Check the OERB for
• (1) Factoring Quadratics-Simple Trinomial, or
• (2) Factoring Quadratics- Difficult Trinomial
  AUSTRALIAN METHOD
• or
• (3) Factoring Quadratics-Difficult Trinomial
  Method of DECOMPOSITION