MYTUTOR SUBJECT ANSWERS

539 views

How to factorise any quadratic expression

Factorising quadratic equations

This method is used for the following factorable expression:

ax2+bx+c

Although this method is particularly useful with quadratic expressions with a≥2, it can be also used when a=1.

Given              ax2+bx+c

Find SUM=b and PRODUCT=ac

Find two numbers p and q, such that p+q=SUM and pq=PRODUCT

The smallest number (without considering the sign), say in this case p, goes into the following bracket:

(ax+p)

The largest number (without considering the sign), say in this case, q, goes into the other bracket:

(x+q/a)

Hence the factorised form is:

(ax+p)(x+q/a)

Further algebra could be used to "tidy" the expression

Example

6x2 - 13x + 5

SUM = b = -13 and   PRODUCT = ac = 6*5 = 30

So p = -3 and q = -10 , as SUM= -3 -10 = -13   and PRODUCT= (-3)*(-10) = 30

As p is the smallest number, this goes in (ax+p) = (6x-3)

And q being the largest, goes into (x+q/a) = (x-10/6)

Hence the factorised form is

 (6x-3)(x-10/6)

or neater (2x-1)(3x-5)

 

Adil P. A Level Chemistry tutor, A Level Physics tutor, A Level Maths...

2 years ago

Answered by Adil, an A Level Maths tutor with MyTutor


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

264 SUBJECT SPECIALISTS

£22 /hr

Sam F.

Degree: Economics with Placement (Bachelors) - Bath University

Subjects offered:Maths, Physics+ 2 more

Maths
Physics
Extended Project Qualification
Economics

“Studying for BSc Hons Economics, A level economics, maths and physics. Able to tutor GCSE/AS/A2 Economics, Maths and GCSE physics! ”

PremiumRyan G. GCSE Maths tutor, GCSE Physics tutor, GCSE Computing tutor, A...
£24 /hr

Ryan G.

Degree: Electrical Engineering with Renewable Energy (Masters) - Edinburgh University

Subjects offered:Maths, Physics+ 2 more

Maths
Physics
Computing
-Personal Statements-

“ I will offer a wide range of ways to learn so you can find a way that best suits you!”

£22 /hr

Shreya G.

Degree: Biochemistry with molecular medicine (Bachelors) - Nottingham University

Subjects offered:Maths, Biology+ 1 more

Maths
Biology
-Personal Statements-

“I am a first year undergraduate student at The University Of Nottingham, currently studying Biochemistry with molecular medicine. ”

About the author

Adil P.

Currently unavailable: no new students

Degree: Chemical Engineering via Natural Sciences (Bachelors) - Cambridge University

Subjects offered:Maths, Science+ 3 more

Maths
Science
Physics
Italian
Chemistry

“Natural Scientist at Cambridge. Maths and chemistry are my forte, but I can help my tutees in Physics.”

You may also like...

Other A Level Maths questions

At x=3, is the polynomial y= (4/3)x^3 -6x^2 + 11 at a maxima or minima?

how do integrate an equation with a surd or a fraction?

Differentiate with respect to x: y=xln(x)

How do I solve equations with modulus functions on both sides?

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