1.
Lesson 2
Objectives
Students should be able to: -
● Factorize simple algebraic expressions using the distributive law
What are factors?
The factors of a given number are those numbers which divide exactly into the given
number. So in other words, factors are what we can multiply to get the number.
2. What is factorisation?
Factorising is finding what to multiply together to an expression! It is like "splitting"
an expression into a multiplication of simpler expressions.
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3. Finding the Highest Common Factor
In the previous example we saw that 2y and 6 had a common factor of 2. But to do the job
properly we need the highest common factor, including any variables
Steps to Factorise
Use the steps to follow how we factorize the example below:
Step 1
Identify the terms in the algebraic expression.
The terms are +10 and +4x
SteP 2
Identify the highest common factor in the given terms. (variables should be accounted
for as well)
The factors for 4x are: 1, 2, 4 and x
The factors for 6 are: 1, 2, 5 and 10
The Highest Common Factor is: 2
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4. Step 3
Divide the common factor into each of the given terms. Term ÷ highest common factor
+10 ÷ 2= 5
+4x ÷ 2= 2x
Step 4
The common factor from step 1 is written outside of the brackets and the quotients from
step 2 are written inside of the brackets paying careful attention to the signs of the
term.
Answer: 2 (5+ 2x)
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5. Let’s look at another example
Factorize 2x+6
Step 1: The terms are: +2x and +6
Step 2: The factors for 2x are: 1, 2 and x
The factors for 6 are: 1, 2, 3 and 6
The highest common factor is:2
Step 3: Each Term ÷ highest common factor
+2x ÷ 2 = x
+6 ÷ 2 = 3
Step 4: Answer: 2(x + 3)
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