how to factorise?

Factorising quadratic equations

To factorise an equation such x2 + 5x + 6, you need to look for two numbers which add up to make 5 and multiply to give 6

The factor pairs of 6 are 1 and 6, 2 and 3

2 and 3 add up to 5

So (x +2 ) (x+3) = x2 + 5x + 6

Factorising expressions gets trickier with negative numbers.

?

Example.

Factorise the expression c2- 3c - 10

  • Write down the equation:
  • c2- 3c - 10
  • Remember that to factorise an expression we need to look for common factor pairs.
  • In this example we are looking for two numbers which:
    • multiply to give -10
    • add to give -3
  • Think of all the factor pairs of -10:
  • 1 and -10, -1 and 10, 2 and -5, -2 and 5

  • Which of these factor pairs can be added to get -3?

  • Only 2 + (-5) = -3

So the answer is:

c2 - 3c - 10 = (c + 2)(c - 5)

1 of 1

Comments

Alice McFarlane

Report

VERY HELPFUL, THANKS :)

Arooj

Report

Thankyou this was quite helpful :) But it could've helped me a bit more  if you had some questions and then answers to them. And given more examples of easy then harder questions of these :D 

daviesg

Report

This is one of the more difficult quadratics to factorise.  A good start however, students might get confused over the use of negatives here.

Similar Mathematics resources:

See all Mathematics resources »See all Algebra resources »