MYTUTOR SUBJECT ANSWERS

495 views

How do you factorise a quadratic equation?

If you are given a simple quadratic equation, for example x2+6x+8=0, then in order to factorise this you must find two numbers that add together to make the coefficient of x in the equation (in this case the coefficient is 6) and multiply together to find the constant (in this case 8).

In order to do this you must find the pairs of factors that multiply together to make the constant, so for this example the factors of +8 are 1&8, 2&4, (-1)&(-8) and (-2)&(-4), then using these factors you have to find a pair that will add together to make the coefficient of x, which we know is 6. Therefore the only pair of factors that will add up to 6 are 2 & 4.

So we place these into brackets like so:
(x+2)(x+4)=0

To check your answer you can simply expand the brackets again, which would give you :
x2+2x+4x+8=0
Simplifying to:
x2+6x+8=0, which is what we originally started with therefore showing that we have factorised correctly.

Factorising quadratics can become more complicated when there are negatives or coefficients of xthat are greater than 1. Solving quadratics with negative signs for example: x2-4x-12=0 is done the same way as before. The factors of -12 are: 1&(-12), (-1)&12, 2&(-6), (-2)&6, 3&(-4) and (-3)&4. Then added together the only factors that make -4 are (-6)&2. Therefore the answer would be (x-6)(x+2)=0

They become even more tricky when the coefficient of x2 is greater than 1. For example: 2x2+5x+2=0. You then have to also consider the factors of the coefficient of x2

The only factors of the constant 2 are 1&2 and (-2)&(-1). However one of the factors in a pair will be multiplied by 2, so these factors become: 2&2, 1&4, (-4)&(-1) and (-2)&(-2). We then need to find out which of these factors add up to 5, which we can see is 1&4.

So our final answer is (2x+1)(x+4).

 

Erin R. GCSE Maths tutor, A Level Maths tutor

2 years ago

Answered by Erin, an A Level Maths tutor with MyTutor


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

295 SUBJECT SPECIALISTS

£20 /hr

Ina H.

Degree: Engineering Science (Masters) - Oxford, Hertford College University

Subjects offered:Maths, Physics+ 2 more

Maths
Physics
Chemistry
.PAT.

“Oxford Engineering student passionate about building thorough understanding from the ground up. Patient, dedicated and keen to see students excel and have fun”

MyTutor guarantee

£20 /hr

Samradnyee K.

Degree: Biomedical Engineering (Bachelors) - Kings, London University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“Hi, I am a Biomedical Engineering student at King’s College London. Mathematics and Physics have always been my passion and I hope to pass on my love for the subjects to you through engaging and interactive sessions specially catered ...”

MyTutor guarantee

£22 /hr

Jonathan D.

Degree: Natural Sciences (Physical) (Bachelors) - Cambridge University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
Chemistry

“2nd year Natural Sciences student at Cambridge - massively passionate about all things Maths and Science, and I would love to be able to help!”

About the author

Erin R.

Currently unavailable: until 17/01/2016

Degree: Mathematics (Bachelors) - Exeter University

Subjects offered:Maths

Maths

“Hi, I'm Erin, a first year maths student at the University of Exeter. I gained an A* in GCSE and A-Level maths meaning that I have the necessary knowledge tohelp you reach your full potential. Maths has always been my favourite subjec...”

MyTutor guarantee

You may also like...

Other A Level Maths questions

how to find flight time/distance and greatest hight of projectiles?

Integrate 8x^3+4 with respect to x.

How does integration work?

How do you prove that (3^n)-1 is always a multiple of 2?

View A Level Maths tutors

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

mtw:mercury1:status:ok