How to factorize in simple steps.

1. HOW TO FACTORIZE

2. To understand factorization, we first simplify
some algebraic expressions
• (x+4)(3x-1)=3x2-11x-4
• (2x-1)(x-3)=2x2-7x-3
• (3c+6)(5c+8)=15c2+54c+48

3. FACTORIZING IS AN ATTEMPT TO FIND THE
ROOT OF AN EXPRESSION
• Factoring Quadratics
• Quadratic Equation
• A Quadratic Equation in Standard Form.
• (a, b, and c can have any value, except that a can't be 0.)
It is called "Factoring" because
we find the factors (a factor is
something we multiply by)

4. Example
Multiplying (x+4) and (3x−1) together (called Expanding) gets 3x2-11x-4 a we
did earlier:
So (x+4) and (3x−1) are factors of + 3x2-11x-4
Just to be sure, let us check:
(x+4)(3x−1) = x(3x−1) + 4(3x−1)
= 3x2 − x + 12x − 4
= 3x2 + 11x − 4, yes
Yes, (x+4) and (x−1) are definitely factors of 3x2-11x-4
(x+4)(3x-1)=3x2-11x-4

5. Step 1: Determine the GCF From an Expression
• Let's consider the following examples and determine the
GCF.
10x2+5x=20
5,2 5 5,4,2
Here, the greatest common
factor is 5
Hence, step 1 completed
Remember, STEP 1:
DETERMINE THE GCF OF
THE EXPRESSION

6. STEP 2: REMOVE THE GCF FROM THE
EXPRESSION
• lets consider the previous expression:
• Let's divide the expression by the GCF which we had
confirmed in the last slide: 5
• Therefore, we get 2x2+x=4
10x2+5x=20
10x2+5x=20
5

7. STEP 3: FACTORIZE BINOMIALS
• Example: what are the factors of 6x2 − 2x = 0 ?
• 6 and 2 have a common factor: 2
• 2(3x 2− x) = 0
• And x2 and x have a common factor: x
• 2x(3x − 1) = 0
• And we have done it!
• The factors are 2x and 3x − 1

8. Therefore, the 2 roots are 0 and 1/3.
• We can now also find the roots (where it equals zero):
when 2x=0
x=0/2
x=0
when 3x-1=0
3x=1
x=1/3

9. Summary: FIND THE GCF
FIND THE ROOTS
(FACTORS=ZERO)
REMOVE THE GCF
FACTORIZE THE
BINOMIAL