MYTUTOR SUBJECT ANSWERS

558 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

269 SUBJECT SPECIALISTS

£20 /hr

Elliot D.

Degree: Mathematics (Bachelors) - St. Andrews University

Subjects offered:Maths, Physics

Maths
Physics

“Hi, I'm a 2nd year Computer Science student at St Andrews University. I mainly teach Maths at both GCSE and A-level.”

£20 /hr

George B.

Degree: Physics with Industrial experience (Masters) - Bristol University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
-Personal Statements-

“I'm a Physics student at the University of Bristol. My passion is Physics and Maths. I love to help people understand what they previously found hard. ”

£24 /hr

Eilidh F.

Degree: Natural Sciences (Bachelors) - York University

Subjects offered:Maths, Further Mathematics + 2 more

Maths
Further Mathematics
Chemistry
Biology

“About me: My name is Eilidh (pronounced Aylee) and I am a student at the University of York. I study Natural Sciences specialising in Neuroscience, and have always loved both Science and Maths. I also reallyenjoy teaching, meeting new...”

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 do you derive the quadratic formula?

Differentiate y= exp(cos^2(x)+sin^2(x)) by using the chain rule.

How do you find the integral of sin^2(x) dx?

Find the shortest distance between the line L: x=1+t, y=1+2t, z=1-t and the point A: (2,3,4)

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