MYTUTOR SUBJECT ANSWERS

225 views

How do I factorise a quadratic equation?

Firstly, make sure you agree that a quadratic equation is an equation of the form y = ax2 + bx + c where a,b,c are (real) constants (a is not 0), and x is the variable. (Note: the equation has an "x squared" term).

An example would be: y = x2 + x - 6.

We want to factorise this equation so we can find the values of x for which y = 0 (the points where the curve crosses the x-axis).

Secondly, we need to be aware that factorising a quadratic mens expressing the equations as a product of two brackets which each contain an term.

So, in the form ax2 + bx + c = (dx + e)(fx + g)

Working with our example, y = x2 + x - 6, we first direct our attention to the constant term c, in this case c = -6.

If we expand the brackets, we get ax2 + bx + c =(dx+e)(fx + g) = dfx2 + (ef +dg)x + eg.

We should already be able to see that for our example where the coefficient of x2 is 1 that d,f = 1 so now we have a simpler equation: 

(x+e)(x+g) = x2 + (e + g)x + eg. (1.1)

We can then use eg = c = -6, our constant term ie. the constant terms in the brackets multiple to make our origanal constant term.

To find e,h, we think of pairs of numbers which multiply to give -6 :

-1 x 6 // -2 x 3 // -3 x 2 // -6 x 1

So how do we decide which pair of number will give the correct equation?

Well we could test each pair and multiply out the brackets until we get the right equation, but this could take some time if we have more than four options, so instead we'll take a shortcut:

See which pairs ​add to give the coefficient of x

From (1.1), we can equate e + g = b.

-1 + 6 = 5 // -2 + 3 = 1 // -3 + 2 = -1 // -6 + 1 = -5

In our example, b = 1, so we can tell that our constants, e,h are -2,+3 and our answer is: y = (x - 2)(x + 3).

Check! (x - 2)(x + 3) = x2 - 2x + 3x - 6 = x2 + x - 6 

as required!

Gemma L. GCSE Maths tutor, A Level Maths tutor, GCSE Physics tutor, A...

8 months ago

Answered by Gemma, a GCSE Maths tutor with MyTutor

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

328 SUBJECT SPECIALISTS

£18 /hr

Jamie L.

Degree: Physics (Masters) - Exeter University

Subjects offered: Maths, Physics+ 1 more

Maths
Physics
Further Mathematics

“Who am I? I am a student at Exeter University, currently studying for a Masters in physics. I began tutoring on a voluntary basis in sixth form, and in time have progressed to being a professional tutor. I have taught GCSEs and A leve...”

£18 /hr

Shelby P.

Degree: Veterinary Science (Bachelors) - Bristol University

Subjects offered: Maths, Human Biology+ 2 more

Maths
Human Biology
Chemistry

“About Me: I am a post-graduate veterinary student in my fourth year at Bristol Univeristy. I graduated from Bristol in 2013 with a First Class Honours in Biological Sciences before starting another degree in Veterinary Sciences so it...”

£18 /hr

Steven A.

Degree: Bioscience (Masters) - Durham University

Subjects offered: Maths, Science+ 5 more

Maths
Science
Human Biology
English
Chemistry
-Personal Statements-

“Hey! I'm Steven, 18 years old and I'm studying Biochemistry at Durham University. I love tutoring people, to put it simply. At my college i was a tutor to a student in the year below me for chemistry and growing up with a younger sist...”

About the author

Gemma L.

Currently unavailable: for regular students

Degree: Mathematics (Bachelors) - Bath University

Subjects offered: Maths, Physics+ 1 more

Maths
Physics
Further Mathematics

“Hi everyone, I'm Gemma. At the moment I am studying (hard) for a Mathematics degree at Bath University. I heave always had a deep love for all things Maths related since I started learning the subject at school. I hope to be able to s...”

MyTutor guarantee

You may also like...

Other GCSE Maths questions

Express 4/(2-√2) in the form a+b√2 and write down the values of a and b.

Mark has a voucher that gives him 22% off the prices at a hardware store. Estimate how much he will pay for an electric drill that normally costs £87.99. (non-calculator) (3)

Given that 346 × 27 = 9342 , work out 34.6 × 2.7

Solve 7(k – 3) = 3k – 5

View GCSE Maths tutors

Cookies:

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

mtw:mercury1:status:ok