MYTUTOR SUBJECT ANSWERS

509 views

How do I factorise quadratic equations?

x2+x-6=y

Is the equation we will use to demonstrate how to factorise quadratics.

The first step involves using the basic shape of all quadratic factorisation:

ax2+bx+c=y

x2+x-6=y

(Cx+A)(Dx+B)=y

We must realize certain equalities that appear between the different expressions of this equation.

1.

Cx*Dx=ax2

C*Dx2=ax2

Cancelling x2

C*D=a

2.

A*B=c

3.

Cx*B+Dx*A=bx

B*Cx+A*Dx=bx

Cancelling x

B*C+A*D=b

This rigid layout can be used to factorise quadratics, but quadratics are all about pattern recognition and a small amount of practice goes a long way.

x2+x-6=y

ax2+bx+c=y

1. As our quadratic has no number multiplying on x^2 the first step of the solution is simple, we know that both C and D are equal to 1 as 1 only has one factor.

C*D=a

C*D=1

1*1=1

2. This is where paths in the solution diverge, as c in our equation, -6, has a number of factors

Those factors are:

+3*-2=-6

-3*+2=-6

+1*-6=-6

-1*+6=-6

A*B=-6

So we know the A and B are one of these factor pairs.

3. B*C+A*D=b

From step 1 in our solution, we know that both C and D are equal to 1. Meaning we can simplify our equation:

A+B=b

A+B=1

Now, from the factors we found in step 2, we must select a pair thats sum equals 1.

+3-2=1, so we know that A=+3 and B=-2 (it is arbritrary which number is assigned to each letter as the rest of the equation is the same).

ax2+bx+c=y

x2+x-6=y

(Cx+A)(Dx+B)=y

C=1

D=1

A=+3

B=-2

x2+x-6=y

(1x+3)(1x-2)=y

Finally, checking our answer:

1x*1x+3x-2x-6=y

x2+x-6=y

Following a rigid method is not recomended for solving quadratics, remember steps and the equalities that must occur, and practice, are the most important things.

Joshua O. A Level Chemistry tutor, A Level Maths tutor, GCSE Maths tutor

2 years ago

Answered by Joshua, who has applied to tutor GCSE Maths with MyTutor


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

434 SUBJECT SPECIALISTS

£20 /hr

Alexander H.

Degree: History (Bachelors) - LSE University

Subjects offered: Maths, History+ 4 more

Maths
History
Geography
English Literature
English Language

“About Myself: My name is Alexander Hawkins and I am 3rd year History student at the London School of Economics (LSE). I have 2 years experience tutoring IB, MYP, and GCSE students. My specific love is 20th century world history, but I ...”

£20 /hr

Amruni C.

Degree: Medicine (Bachelors) - Imperial College London University

Subjects offered: Maths, Science+ 1 more

Maths
Science
-Medical School Preparation-

“Hi, I’m Amruni and I’m a medical student at Imperial College London. For the past 2 years I have been tutoring Maths and Science to students from 11+ to GCSE and have absolutely loved being able to share my passion for science and mat...”

£18 /hr

Dhulaxy M.

Degree: Biological Sciences (Bachelors) - University College London University

Subjects offered: Maths

Maths

“I am currently a first-year Biology student at University College London. I love that my course brings in aspects of the other ‘science’ subjects, especially Maths! I have volunteered in environments like the library and nursing home ...”

MyTutor guarantee

About the author

£18 /hr

Joshua O.

Degree: Chemistry Msci (Masters) - Queen's, Belfast University

Subjects offered: Maths, Chemistry

Maths
Chemistry

“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

MyTutor guarantee

You may also like...

Posts by Joshua

How do I factorise quadratic equations?

How do I use the chain rule to differentiate polynomial powers of e?

What is Effective Nuclear Charge?

Other GCSE Maths questions

If f(x) = 4x - 7 and f(c) = 9, find the value of c.

How do I factorise x^2 ​- 4?

How do I find the length of a side of a triangle using the cosine rule?

What is the easiest way to expand quadratic equations?

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