Algebra - Factorising

Question 1

What is factorising?

Answer 1

Factorising is the skill of splitting something into its factors.

Question 2

Type 1 - Removing a common factor

Answer 2

Eg - 3x+6

= 3(x+2)

Question 3

Type 2 - Factorising quadratics in the form ax squared + bx + c

-How do we do this?

Answer 3

To factorise quadratics in the form ax squared + bx + c we need to find 2 numbers which have a product of ‘a times c’ and a sum of ‘b’.

Question 4

What do we do when ‘ax’ is a number and x, and not just x squared on its own?

Answer 4

When ‘a’ is a number and not just x squared on its own we should have the 2 outside terms and 2 inside terms multiply to equal the two numbers which multiply to give the product and add to give the sum.

Question 5

Type 3 - Difference of two squares (DOTS)

Answer 5

If an expression is in the form ‘a squared - b squared’ it can factorised as follows:

a squared - b squared = (a+b)(a-b)

Eg - x squared - 9
= (x+3)(x-3)

Question 6

Type 4 - Four term factorising

-How does four term factorising work?

Answer 6

Four term factorising works by splitting the middle term.

Eg - ax+ay+bx+by
=a(x+y)+b(x+y)
=(x+y)(a+b)

Question 7

What do we do when we are unable to find a common factor in a four term factorising question? (Where applicable)

Answer 7

When we are unable to find a common factor in a four term factorising question, we should see if we can swap around the terms to get common factors on both sides.