Hey there! Sign in to join this conversationNew here? Join for free
x Turn on thread page Beta
    • Thread Starter


    I'm looking at the equation x^2 + 2x - 8 = 0

    I know you get (x + 4)(x - 2) = 0 but I don't get why we use two numbers multiplied together to make 8 (or whatever number it is). Then, those same two numbers add up to the 2 (in the 2x).

    Is there a better explanation than it just works this way?


    What is happening here is that you are changing three things that add up (x squared two x and minus 8) to two thing that multiply. (X+4 and x-2). If two thing multiply to make zero then the only way that can happen is if one of the things in the multiply is zero. Hence the either x+4=0. OR the x-2 =0). In its original form where three things ADDED to make zero, you could not really do anything.

    In other words, the original sum and the pair of brackets are two ways of saying exactly the same thing (called an identity). The method of multiplying the brackets back out is that everything in the left hand bracket has to multiply everything in the right hand brackets and the result must equal the original three part expression.

    Does the above take you anywhere forward?

    (x+4)(x-2) Let's multiply these together

    So FOIL
    First - x * x gives x^2
    Outer - x * -2 gives -2x
    Inner - +4 * x gives +4x
    Last - +4 * -2 gives -8 <- this is the multiplication to get the minus 8

    the outer and the inner are your x terms.
    So we add -2x and +4x together to get the +2x

    Notice how they keep reappearing. The factors add to give the x term, and multiply to give the integer term
    • Community Assistant

    Community Assistant
    Maybe try box multiplication to understand it better.
Have you ever experienced racism/sexism at uni?
Useful resources

Make your revision easier


Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here


How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.