True or false?

Factorising is the opposite of expanding (distributing).

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)**

What is the GCF (greatest common factor)?

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)

What is the GCF of 24, 36 and 48?

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**

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

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**.

What is the GCF of 35y^{4}, 14y^{4}, and 63y^{3}?

- 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.
- 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 y
^{3}out of all of them. - This means the GCF is 7y
^{3}.

What is the GCF of 30b^{2}a, 80b^{2}c, and 20b^{3}?

- 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.
- 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 b
^{2}out of all of them. - This means the GCF is 10b
^{2}.

How do you factorise

2x + 2?

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!)

Factorise 6x + 12

The GCF of 6x + 12 is 6:

6x + 12 = **6(x + 2)**

Factorise 2x^{2} + 4x

The GCF of 2x^{2} + 4x is 2x

(remember that x^{2} = (x) (x))

So 2x^{2} + 4x = **2x(x + 2)**

Factorise 12x^{2} + 18x

The GCF of 2x^{2} + 4x is 2x

(remember that x^{2} = (x) (x))

So 12x^{2} + 18x = **2x(x + 2)**