710 views

### How do you factorise a quadratic equation?

A quadratic expression is of the form ax​2+bx+c. It is often useful to know what values of x will make the expression equal to 0; these are known as the roots of the equation. An easy way of seeing what these roots are is by factorisation of the equation (note that quadratic equations cannot always be factorised).

Starting with the general equation ax​2+bx+c = 0 we must look for a pair of numbers whose sum is equal to b and whose product is equal to c. So in the example x​2+2x+1 = 0 that would be 1 and 1, as 1+1 = 2 = b and 1x1 = 1 = c.

Once you have determined what the pair of numbers are you can put them into brackets like so: x​2+2x+1 = (x+1)(x+1).

Now for a second example where one of the numbers is negative. If x2​+2x-8 = 0 then the pair of numbers which add to 2 and multiply to give -8 is 4 and -2. We can now rewrite this in brackets as x2​+2x-8 = (x+4)(x-2).

2 years ago

Answered by Tim, a GCSE Maths tutor with MyTutor

## Still stuck? Get one-to-one help from a personally interviewed subject specialist

#### 533 SUBJECT SPECIALISTS

£20 /hr

Xanthe W.

Degree: Biological Sciences with a Year in Industry/Research (Bachelors) - Imperial College London University

Subjects offered:Maths, Chemistry+ 1 more

Maths
Chemistry
Biology

£24 /hr

Roma V.

Degree: Mathematics, Operational Research, Statistics and Economics (Bachelors) - Warwick University

Subjects offered:Maths, Further Mathematics + 1 more

Maths
Further Mathematics
Economics

£24 /hr

Victoria S.

Degree: Physiology (Bachelors) - Liverpool University

Subjects offered:Maths, Biology

Maths
Biology

“Here to help with last minute revision prep! I'm Tory, in my final year studying Physiology at Uni of Liverpool and am a 5* rated tutor here to suit your needs.”

Tim W.

Currently unavailable: for new students

Degree: BSc Mathematics (Bachelors) - Cardiff University

Subjects offered:Maths

Maths

“I am a mathematics student at Cardiff University and a friendly individual who is very patient. I have been teaching classical guitar for a year to a range of ages from 8 to 15 and so have experience as a teacher.”

### You may also like...

#### Posts by Tim

How do you differentiate parametric equations?

How do you factorise a quadratic equation?

How do you integrate by parts?

#### Other GCSE Maths questions

Solve the simultaneous equations: y=x/2 + 2 and 2y+3x=12

What is the difference between a histogram and a bar chart? How can I find the frequency density?

Pythagoras: If you have a right angled triangle PQR, and length PQ=5cm, length QR=8cm (which is the longest length), then calculate length PR to two decimal places.

If x+y=100, x is a square number and y is a prime number, find the values of x and y.

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this.