Factorising

Question 1

True or false?

Factorising is the opposite of expanding (distributing).

Answer 1

True!

When you factorise, your aim is to create binomials with brackets around them with a factor outside.

e.g.

2x + 2 = 2(x+1)

Question 2

What is the GCF (greatest common factor)?

Answer 2

The greatest common factor (GCF) is the largest number that divides evenly into all of the numbers.

e.g.

The GCF of 6, 12, and 18 is 6.

(3 is also a factor, but it’s smaller than 6, and we want the biggest commong factor)

Question 3

What is the GCF of 24, 36 and 48?

Answer 3

Factors for 24, 36, and 48

include: 1, 2, 3, 4, 6, and 12 (all of these divide evenly in all three numbers)

So the GCF is 12

Question 4

What is the GCF of 2x, 3x, and 5x?

Answer 4

Here the ONLY factor of 2x, 3x, and 5x is just x! No number (other than 1) divides evenly in 2, 3 and 5.

So GCF is 1x, or just x.

Question 5

What is the GCF of 35y⁴, 14y⁴, and 63y³?

Answer 5

1. Look at the numbers. What’s the greatest common factor of 35, 14, and 63. Well, 7 is the biggest factor of each term, so that must be 7.
2. Look at the variables. Every term has at least one y, so y must be a factor. And the smallest exponent is 3, so we can factor y³ out of all of them.
3. This means the GCF is 7y³.

Question 6

What is the GCF of 30b²a, 80b²c, and 20b³?

Answer 6

1. Look at the numbers. What’s the greatest common factor of 30, 80, and 20. Well, 10 is the biggest factor of each term, so that must be 10.
2. Look at the variables. Every term has at least one b, so b must be a factor. And the smallest exponent fpr b is 2, so we can factor b² out of all of them.
3. This means the GCF is 10b².

Question 7

How do you factorise

2x + 2?

Answer 7

Find the GCF and “take it out” of each term by dividing (and you “group” what’s left inside a bracket):

GCF of 2x + 2 is just 2.

2x + 2 = 2(x + 1)

If you were to expand the bracket again, you should have what you started off with. 2(x+1) = 2(x) + 2(1) =

2x + 2 (it works!)

Question 8

Factorise 6x + 12

Answer 8

The GCF of 6x + 12 is 6:

6x + 12 = 6(x + 2)

Question 9

Factorise 2x² + 4x

Answer 9

The GCF of 2x² + 4x is 2x

(remember that x² = (x) (x))

So 2x² + 4x = 2x(x + 2)

Question 10

Factorise 12x² + 18x

Answer 10

The GCF of 2x² + 4x is 2x

(remember that x² = (x) (x))

So 12x² + 18x = 2x(x + 2)