Lesson 2-3 Factoring Polynomials
EXPANDING
5x(x-3)
=
5x2 - 15x
Factoring is the opposite of expanding. To factor means
expressing a number as a product of 2 numbers or an
algebraic expression as a product of two or more algebraic
expressions.
FACTORING
A. GREATEST COMMON FACTOR (GCF)
Ex 1 Factor
a) 5x2 - 15x
b) 3x3y3 – 12xy5 +6x2y4
B. FACTORING BY GROUPING
Ex 2 Factor by grouping:
a) 𝑓(𝑥) = 𝑛3 + 3𝑛2 + 2𝑛 + 6
b) 𝑓(𝑥) = 𝑥 3 + 𝑥 2 + 𝑥 + 1
C. FACTORING SIMPLE TRINOMIALS (x2+ bx + c)
Ex. 3
Factor
2
a) x + 7x + 10
Find two numbers that:
- add to give you “b”
- multiply to give you “c”
b) x 2  5xy  14 y 2
D. FACTORING COMPLEX TRINOMIALS (ax2+ bx + c)
Decomposition:
Ex. 4 Factor 6 y 2  26 y  20




Remove the G.C.F.
Find two numbers whose
sum = “b” and whose
product = “ a  c ” and
expand your trinomial using
those two numbers (decompose
the middle number)
group the terms and factor each
group
X-Method:


Remove the G.C.F.
Find two numbers that multiply to give “a” and 2 other numbers that multiply to
give “c”.
Ex. 5
Factor
2
a) 12x + 10x -50
b) 3m 2  19mn  20n 2
E. FACTORING A DIFFERENCE OF SQUARES
A difference of squares is a binomial that satisfies the following conditions:
 Each term is a perfect square
a 2  b 2  (a  b)( a  b)
 Has a subtraction sign between the two terms
Ex. 6
Factor
2
a) 4x – 9
b) 2a - 8a3
c) 𝑓(𝑥) = 𝑥 2 − 6𝑥 + 9 − 4𝑦 2
d) 5a2 – 20(b-3)2
F. FACTORING A PERFECT SQUARE TRINOMIAL
A perfect square trinomial (P.S.T) is a trinomial that satisfies the following conditions:
 1st and 3rd terms are positive and perfect squares
a 2  2ab  b 2  (a  b) 2
st
rd
 middle term = 2 1 term 3 term
a 2  2ab  b 2  (a  b) 2
Ex. 7: Factor
a) x2 + 20x + 100
b) 4x2 -12x +9
Homework: Pg. 102 # (1-7, 9) odds, 12 a
c) 4x2 -28xy + 49y2