Review: Perfect Square
(x² + 8x + 16)
Remember, a PST factors into either a square of
a sum or a square of a difference.
Use the FOIL method to factor the following:
(x² + 4x + 4x + 16) = (x + 4)²
(x² - 16x + 64) (x² - 8x - 8x + 64) = (x - 8)²
(x² - 15x + 36) (x² - 12x - 3x + 36) = Is not a sp. product.
A trinomial with first & third term squares is only a
PST if... 9y3 + 12x2 +
PST or no PST?
Steps in factoring completely:
1. Look for the GCF
2. Look for special cases.
a. difference of two
b. perfect square
3. If a trinomial is not a
perfect square, look for
two different binomial
8t4 – 32t3 + 40t
= 8t(t3 - 4t + 5)
4x2 – 9y2 =
(2x)2 – (3y)2
x2 + 8x + 16 =
x2 + 8x + 42 = (x + 4)2
x2 + 11x – 10
= (x + 10)(x – 1)
An organized approach to factoring
2nd degree trinomials
+ bx + c) Trinomials
Use this algorithm (procedure) to take the
guesswork out of factoring trinomials.
It would be a good idea to write the steps down
once, as they are easy to forget when away
You can use these steps for any ax2
+ bx + c
polynomial, and for any polynomial you are
having difficulty factoring.
Multiply the leading coefficient and the constant
Find the two factors of 24 that add to
the coefficient of the middle term.
Notice the 'plus, plus' signs in the
Factors of 24:
Our two factors are 4 &
Re-write the original trinomial
and replace 10x with 6x + 4x.
+ 6x + 4x + 8
4 Factor by Grouping
Factor out the GCF of each pair of
After doing so, you will have...
Step 6 Factor out the common binomial,
check that no further factoring is
possible, and the complete