### Understanding Factorization:

Let’s start by explaining the reverse of factorization. Consider the equation below:

(4a + 6)(a – 1)

We can see 4 values from the above equation, they are:

4a, 6, a and -1

If we were to expand the brackets, we will have to:

• Multiply +4a by a ….. '+4a x a' = 4a2

• Multiply +4a by -1 ….. '+4a x -1' = -4a

• Multiply +6a by a ….. '+6 x a' = +6a

• Multiply +6a by – 1 ….. '+6 x -1' = -6

Note the followings:

1. Minus x Plus = Minus
2. Plus x Minus = Minus
3. Minus x Minus = Plus
4. Plus x Plus = Plus

Understand that when there isn't a sign in front of a number or variable, then it is considered to have a plus sign (+) before it.

If there isn’t any number in front of a variable, then it’s considered to have the value '1' before it. For instance ('a' has the same value as '1a').

The result from expanding (4a + 6)(a – 1) will give us:

(+4a x a) (+4a x -1) (+6 x a) (+6 x -1)

4a2 – 4a + 6a - 6

Since -4a and +6a are like terms (–4a + 6a will give us +2a), we will have our answer to be:

4a2 + 2a - 6

If you understood the above example, then factorization will become easier for you.

Factorization is simply the reverse of expanding brackets.

You may have to make some trials and errors when solving certain factorization questions, but following the steps in my examples will make factorization questions easier for you.

#### Example 1:

Factorize 4b2 – 10b + 4

We have three values from the question. They are:

+ 4b2, -10b, and +4

To factorize the above equation, we will need to split the middle value into 2 numbers whose:

• Addition or Subtraction will be equal to -10b

• Product will be equal to the 16b2 (that is, the product of 4b2 and 4 (at the right side).

(-8b – 2b) will work for us because:

• Their subtraction = -10b

• Their multiplication = 16b2

4b2 – 8b – 2b + 4

Notice that 4b2 and 8b are divisible by '4b', (that is, 4b is a factor) while 2b and 4 are divisible by 2, (that is, 2 is a factor). Therefore we can write:

4b(b - 2) -2(b - 2)

Now the brackets are the same, so our answer is:

Answer = (4b - 2)(b - 2)

#### Example 2:

Factorize 12a² - 20a + 3

To factorize the above equation, we will need to split the middle value into 2 numbers whose:

• Addition or Subtraction will be equal to -20a

• Product will be equal to 36a² (that is, the product of 12a2 and 3 (at the right side).

-18a – 2a will work for us because:

• Their subtraction = -20a

• Their multiplication = 36a²

12a2 – 18a – 2a + 3

Notice that 12a2 and 18a are divisible by '6a', (that is, 6a is a factor) while 2 and 3 are not divisible. Therefore we can write:

6a(2a - 3) -1(2a - 3)

Now the brackets are the same, so our answer is:

Answer = (6a - 1)(2a - 3)

#### Example 3:

Factorize d² + 2d - 8

To factorize the above equation, we will need to split the middle value into 2 numbers whose:

• Addition or Subtraction will be equal to +2d

• Product will be equal to the 8d² (that is, the product of d2 and 8 (at the right side).

+4d - 2d will work for us because:

• Their multiplication = 8d²

d2 + 4d - 2d + 8

Notice that d2 and 4d are divisible by 'd', (that is, d is a factor) while 2d and 8 are divisible by '2', (that is, 2 is a factor), Therefore we can write:

d(d + 4) -2(d + 4)

Now the brackets are the same, so our answer is:

Answer = (d - 2)(d + 4)

Alfred Ajibola is a Medical Biochemist, a passionate Academician with over 7 years of experience, a Versatile Writer, a Web Developer, a Cisco Certified Network Associate and a Cisco CyberOps Associate.

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