Factorizing Algebraic Expressions Worksheet

ADVERTISEMENT

Worksheet 2.6 Factorizing Algebraic Expressions
Section 1
Finding Factors
Factorizing algebraic expressions is a way of turning a sum of terms into a product of smaller
ones. The product is a multiplication of the factors. Sometimes it helps to look at a simpler
case before venturing into the abstract. The number 48 may be written as a product in a
number of different ways:
48 = 3 × 16 = 4 × 12 = 2 × 24
So too can polynomials, unless of course the polynomial has no factors (in the way that the
number 23 has no factors). For example:
3
2
3
2
6x
+ 12x
8 = (x
2)
= (x
2)(x
2)(x
2) = (x
2)(x
4x + 4)
x
3
where (x
2)
is in fully factored form.
Occasionally we can start by taking common factors out of every term in the sum. For example,
2
2
3xy + 9xy
+ 6x
y = 3xy(1) + 3xy(3y) + 3xy(2x)
= 3xy(1 + 3y + 2x)
Sometimes not all the terms in an expression have a common factor but you may still be able
to do some factoring.
Example 1 :
2
2
2
2
9a
b + 3a
+ 5b + 5b
a = 3a
(3b + 1) + 5b(1 + ba)
Example 2 :
2
10x
+ 5x + 2xy + y = 5x(2x + 1) + y(2x + 1)
Let T = 2x + 1
= 5xT + yT
= T (5x + y)
= (2x + 1)(5x + y)
Example 3 :
2
3
2
2
+ 2xy + 5x
+ 10x
y = x(x + 2y) + 5x
(x + 2y)
x
2
= (x + 5x
)(x + 2y)
= x(1 + 5x)(x + 2y)

ADVERTISEMENT

00 votes

Related Articles

Related forms

Related Categories

Parent category: Education