 
Combinations
Sometimes, in order to factorise an expression as fully as possible,
you need a combination of quadratic factorisation with the taking out of other common
factors.
Example
10 

2x^{2}(x + 1)  4x 
Strategy 
2x is in common.
2x^{2}(x + 1)
 4x
= 2x(x(x + 1)  2(2x))
= 2x(x(x + 1)  2)
= 2x(x^{2} + x  2) 
Factorise by taking out common factors first.
Try to simplify the expression in the brackets. If it is a quadratic expression,
try to factorise it. 
For x^{2}
+ x  2, A = 1, B = 1, C = 2^{} 
Obtain the values of A, B and
C by inspection 
Hence x^{2} + x  2
= (x  1)(x + 2)

Substitute the values into
the quadratic formula and simplify.
To make the factorisation correct we have to multiply by the coefficient
of x^{2} in the original quadratic, that is multiply by A. (No action
is required if A = 1.) 
2x^{2}(x + 1)  4x = 2x(x  1)(x + 2) 
Put it all together. 
Now try your hand at some really tough examples!
Exercise
10
Factorise each expression as far as possible. 

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