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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.

CxB+DxA=bx

BCx+ADx=bx

Cancelling x

BC+AD=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. BC+AD=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.

Answered by Joshua O. Maths tutor

1294 Views

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Answered by Joshua O.
Maths tutor

1294 Views

See similar Maths GCSE tutors
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