evaristegalois
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How many ways are there to factorise quadratics?
Name me them, and tell me how you do them, thanks! (I've heard of grouping before) :cool::p:D:confused:
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cooldudehjhjwbjd
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(Original post by evaristegalois)
How many ways are there to factorise quadratics?
Name me them, and tell me how you do them, thanks! (I've heard of grouping before) :cool::p:D:confused:
One method of factorising a quadratic is to list the numbers which need multiplying or you can see certain patterns in a quadratic which can help with these. Example quadratic factorisation
x2+6x-16
(x+8) (x-2)

First of all this equation involves indices and a certain amount of x's with a specific digit. Usually this sort of format will involve the use of two brackets

Here's another example
5x+2x2-3x72x(2.5+2x-1.5x6)

I have realised I have complicated this a bit-it will be much easier in the exam, but you get the idea. Normally these sort of equations involve an x somewhere
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morgan8002
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(Original post by evaristegalois)
How many ways are there to factorise quadratics?
Name me them, and tell me how you do them, thanks! (I've heard of grouping before) :cool::p:D:confused:
If the roots are rational, you can usually factorise a quadratic by inspection. ax^2+bx+c. List all of the factors of a and c and try out each combination until you get one that expands to the quadratic you need.

A special case is when you have a quadratic of the form x^2 - a^2. You can factorise this by difference of two squares. Factorised it is(x+a)(x-a).

If the roots are complex or irrational, complete the square or use the quadratic formula to find the roots(although quadratics of this type aren't usually put into a factorised form).
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wilcolly
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(Original post by evaristegalois)
How many ways are there to factorise quadratics?
Name me them, and tell me how you do them, thanks! (I've heard of grouping before) :cool::p:D:confused:
Morgan seems to have covered most ways to factor quadratics complete the square, difference of two squares, quadratic formula or by inspection (see first post) if you are simply looking for the roots of the equation the quadratic formula will always supply error free solutions!
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evaristegalois
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Yes but how would I factorise a quadratic equation that looks like this?

2x^2+5x+3=0

Notice the the "2x^2"
and wow how did you add them maths characters.
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morgan8002
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(Original post by evaristegalois)
Yes but how would I factorise a quadratic equation that looks like this?

2x^2+5x+3=0

Notice the the "2x^2"
and wow how did you add them maths characters.
List the factors of 2: 2, 1
List the factors of 3: 3, 1
Because each has only two factors(is prime) we now know that:
There's a 2x in one bracket and x in the other.
There's a 3 in one bracket and a 1 in the other.
You could now try each combination until you find one that works or you can follow the next steps.

The coefficient of x in the quadratic is 5, so I have to find a way of factorising based on the combinations I have. It springs to mind that 2+3=5. Remember that the coefficient of x in one bracket is multiplied by the constant in the other bracket . I can make 5 by 2x1 + 1x3, so (2x+3)(x+1).


LaTeX. There's a guide on how to do it if you type latex into the search bar.
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