3.
3
Review: Perfect Square
Trinomial
(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 +
4x
PST or no PST?
4.
Steps in factoring completely:
1. Look for the GCF
2. Look for special cases.
a. difference of two
squares
b. perfect square
trinomial
3. If a trinomial is not a
perfect square, look for
two different binomial
factors.
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)
5.
An organized approach to factoring
2nd degree trinomials
5
Factoring (ax2
+ bx + c) Trinomials
6.
Factoring 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
from class
You can use these steps for any ax2
+ bx + c
polynomial, and for any polynomial you are
having difficulty factoring.
7.
Step 1
7
Multiply the leading coefficient and the constant
term
8.
Step 2
8
Find the two factors of 24 that add to
the coefficient of the middle term.
Notice the 'plus, plus' signs in the
original trinomial.
Factors of 24:
1 24
2 12
3 8
4 6
Our two factors are 4 &
6
9.
Step 3
9
Re-write the original trinomial
and replace 10x with 6x + 4x.
3x2
+ 6x + 4x + 8
Step
4 Factor by Grouping
10.
Step
5
10
Factor out the GCF of each pair of
terms
After doing so, you will have...
Step 6 Factor out the common binomial,
check that no further factoring is
possible, and the complete
factorization is..
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