Mathematics
For each trinomial (quadratic expression), given below, find whether it is factorisable or not. Factorise, if possible.
(i) x2 - 3x - 54
(ii) 2x2 - 7x - 15
(iii) 2x2 + 2x - 75
(iv) 3x2 + 4x - 10
(v) x(2x - 1) - 1
Factorisation
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Answer
(i) Given,
x2 - 3x - 54
= x2 - 9x + 6x - 54
= x(x - 9) + 6(x - 9)
= (x - 9)(x + 6).
Hence, the above equation is factorisable and x2 - 3x - 54 = (x - 9)(x + 6).
(ii) Given,
2x2 - 7x - 15
= 2x2 - 10x + 3x - 15
= 2x(x - 5) + 3(x - 5)
= (2x + 3)(x - 5).
Hence, the above equation is factorisable and 2x2 - 7x - 15 = (2x + 3)(x - 5).
(iii) Given,
2x2 + 2x - 75
Hence, the above equation is not factorisable.
(iv) Given,
3x2 + 4x - 10
Hence, the above equation is not factorisable.
(v) Given,
x(2x - 1) - 1
= 2x2 - x - 1
= 2x2 - 2x + x - 1
= 2x(x - 1) + 1(x - 1)
= (x - 1)(2x + 1).
Hence, the above equation is factorisable and x(2x - 1) - 1 = (x - 2)(2x + 1).
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