883 views

### How to factorise simple quadratic equations?

The reason why we factorise quadratic equation is because it is a neater and simpler way of writing the expression.

Example 1

If we wanted to factorise x^2 + 10 + 21 we must look at factors of 21 that add up to 10.

The factors are:

7 and 3

21 and 1

It is clear that the factors 7 and 3 add up to 10, thus they are the factors that we shall use.

Therefore we can write (x+7)(x+3) = x^2 + 10x + 21

Example 2

If the question has the form of x^2 - bx + c such as x^2 - 10x +21, we use the same technique as example one and thus the factors are -7 and -3 (note they add up to -10).

Finally this means x^2 - 10x + 21 = (x-7)(x-3)

Example 3

If the equation has the form x^2 + bx - c such as x^2 + 4x - 21.

As above we find the factors of 21 BUT now we find the difference of the two factors to obtain 4.

The rule tends to be if the middle number is positive the larger factor is positive and if the middle number is negative the larger factor is negative.

(x+7)(x-3) = x^2 + 4x - 21

Also note:

(x-7)(x+3) = x^2 - 4x - 21

2 years ago

Answered by Karan, a GCSE Maths tutor with MyTutor

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

#### 654 SUBJECT SPECIALISTS

£36 /hr

Degree: Economics with French (Bachelors) - Bristol University

Subjects offered:Maths, Spanish+ 2 more

Maths
Spanish
French
Economics

“Private tutor of Economics, Maths and French with six years of experience. I am passionate about teaching!”

£30 /hr

Degree: Dentistry (Masters) - Leeds University

Subjects offered:Maths, Science+ 12 more

Maths
Science
Mandarin
Human Biology
English Literature
English Language
Chemistry
.UKCAT.
-Personal Statements-
-Oxbridge Preparation-
-Medical School Preparation-

“Hi I'm Vicky, I'm a 2nd year dental student at the University of Leeds. I am friendly and patient and have a love for science, maths and teaching.”

£20 /hr

Degree: Biomedical Sciences (Bachelors) - Cardiff University

Subjects offered:Maths, Russian+ 1 more

Maths
Russian
English

“Hopeful doctor in the making looking to help you reach your goals! I'm interested in everything so I am sure we will have something in common.”

£18 /hr

Degree: Maths (Bachelors) - Birmingham University

Subjects offered:Maths, Physics

Maths
Physics

“Hi, I'm Karan and I am a recent graduate in Mathematics from University of Birmingham with a First Class Honours. I thoroughly enjoy tutoring Maths at GCSE and A-Level and I'm determined to help you achieve your goals! ”

MyTutor guarantee

### You may also like...

#### Posts by Karan

How to factorise simple quadratic equations?

How to integrate a simple expression

#### Other GCSE Maths questions

Solve the simultaneous equations 2x + 3y = 4, 3x + 6y = 3

How do I solve a simple simultaneous equation?

Sam uses 140g of flour to make 12 cakes. How much flour will Sam need to make 21 cakes?

Solve for simultaneous equations x +5y =9 and 3x + 2y =5.

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