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Factorisation - Factors of the Form ( x + a) ( x + b)

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Let us now discuss how we can factorise expressions in one variable, like `x^2 + 5x + 6, y^2 – 7y + 12,  z^2 – 4z – 12, 3m^2 + 9m + 6,` etc. 
Observe that these expressions are not of  the type `(a + b)^2` or `(a – b)^2`, i.e., they are not perfect squares.
In general, for factorising an algebraic expression of the type 
`x^2 + px + q,` we find two factors a and b of q (i.e., the constant term) such that
ab = q    and     a + b = p 
Then, the expression becomes  `x^2 + (a + b) x + ab` 
or `x^2 + ax + bx + ab` 
or x(x + a) + b(x + a) 
or (x + a) (x + b)             which are the required factors.

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