How do you factorise a quadratic?

A quadratic equation is something that looks like this: ax2+bx+c. FACTORISING a quadratic means to put this equation in the form (dx+e)(fx+g). For example, take the equation x2+5x+6. The factorised form of this equation is (x+2)(x+3). How do we get here? First, let us look at the above example. Notice that 2+3=5, and 23=6. In this case, we found two numbers that add up to 5 and multiply to make 6. Now let's go through the steps for factorising quadratics. Let's use a new example, 6x2-x-2. 1. Look at the coeffient (number in front) of x2. In our case, it is 6. We can factorise 6 in two ways: 61 and 32. Let's test 32 by writing some brackets like so: (3x  )(2x  ). 2. We need to find two numbers that multiply to give -2. Well, 1*-2=-2, so let's see if 1 and -2 work in our brackets. 3. We check if the numbers, 1 and -2, work by seeing whether 31+2-2=-1. Well, 31=3 and 2-2=-4, and adding these indeed gives -1. So we are done, and the final answer is: 6x2-x-2 = (3x-2)(2x+1).

Answered by Ethan B. Maths tutor

2713 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Expand and simplify (x-2)(2x-3)(x+1)


The diagram shows the position of two ships, A and B, and a lighthouse L. Ship A is 5km from L on a bearing of 070° from L. Ship B is 3km from L on a bearing of 210° from L. Find the distance between A and B correct to 3.s.f.


Make x the subject 2x+3=3x-1


A quadrilateral has a perimeter of 42cm. Three sides have equal length and the fourth side is longer by 6cm. What is the length of the fourth side?


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2024

Terms & Conditions|Privacy Policy
Cookie Preferences