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How do you factorise a quadratic equation?

Often quadratic equations of the form ax2+bx+c=0 can be easily solved by factorising. First, find pairs of numbers that multiply together to make c. Note that if c is positive, the two numbers will have the same sign, and if c is negative, the two numbers will have different signs.

Eg. if the equation is x2+5x-6, the pairs could be: 1 and -6, -1 and 6, 2 and -3, or -2 and 3.

Secondly, check each pair until you find which pair add together to make b. In the case of the example above, this is -1 and 6. If is something other than 1, you will either need to multiply one of the numbers in the pair by a, or multiply each number by a factor of a. In your exam you are unlikely to be given anything more complicated than a being 1,2 or 3.

Once you have the two numbers, simply put them in brackets: (x-1)(x+6)=0, (in the case of the above example). The solutions are then: x=1 or x=-6

Matt M. A Level Physics tutor, GCSE Physics tutor, GCSE Chemistry tut...

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