MYTUTOR SUBJECT ANSWERS

300 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

175 SUBJECT SPECIALISTS

£22 /hr

Daniel F.

Degree: Maths and Philosophy (Bachelors) - Durham University

Subjects offered: Maths, Further Mathematics

Maths
Further Mathematics

“Friendly and Enthusiastic Maths and Philosophy student at Durham University”

£22 /hr

Bryan P.

Degree: Mathematics (Bachelors) - Bristol University

Subjects offered: Maths, Further Mathematics

Maths
Further Mathematics

“I am currently a BSc Mathematics student at the University of Bristol and I am already no stranger to teaching.I have worked as a teaching assistant in my secondary school's maths department where I also led one-on-one sessions with ...”

£22 /hr

Jordan H.

Degree: MPhys Physics with Professional Experience (Masters) - Exeter University

Subjects offered: Maths, Physics+ 2 more

Maths
Physics
Chemistry
Biology

“Hi, I'm Jordan, a first year Physics undergraduate hoping to help both A-level and GCSE students in Maths and Physics.”

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

Using the addition formula for sin(x+y), find sin(3x) in terms of sin(x) and hence show that sin(10) is a root of the equation 8x^3 - 6x + 1

A cup of coffee is cooling down in a room following the equation x = 15 + 70e^(-t/40). Find the rate at which the temperature is decreasing when the coffee cools to 60°C.

A curve is described by the equation x^3 - 4y^2 = 12xy. a) Find the points on the curve where x = -8. b) Find the gradient at these points.

What is the natural logarithm?

View A Level 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