MYTUTOR SUBJECT ANSWERS

617 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

325 SUBJECT SPECIALISTS

£26 /hr

Priya L.

Degree: Economics (Bachelors) - Warwick University

Subjects offered:Maths, Further Mathematics + 1 more

Maths
Further Mathematics
Economics

“My goal is to elevate the confidence of students by ensuring they truly understand Maths at GCSE and A Level”

£20 /hr

Adamos S.

Degree: Electrical and Electronic Engineering (Masters) - Imperial College London University

Subjects offered:Maths, Further Mathematics + 1 more

Maths
Further Mathematics
Electronics

“Degree: Electrical and Electronic Engineering (Masters) University: Imperial College London”

£26 /hr

Scott R.

Degree: PGCE Secondary Mathematics (Other) - Leeds University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“I am currently completing 2 PGCEs in Leeds. I have always had a passion for maths and my objective is to help as many as possible reach their full potential.”

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

Express x^2 + 5x + 10 in the form (x+p)^2 +q

Use the chain rule to differentiate y=1/x^2-2x-1

y = x*(x-2)^-1/2. Prove dy\dx = (x-4)/2*(x-2)^3/2

Differentiate y = x^3 +x^2 - 4x +5 with respects to x.

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