Mathematics
Factorise the following:
60x2 - 70x - 30
Factorisation
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Answer
60x2 - 70x - 30 = 10(6x2 - 7x - 3).
To factorise 6x2 - 7x - 3, we want to find two real numbers whose sum is -7 and product is 6 × (-3) = -18. By trial, we see that (-9) + 2 = -7 and (-9) × (2) = -18.
∴ 6x2 - 7x - 3 = 6x2 - 9x + 2x - 3
= 6x2 - 9x + 2x - 3
= 3x(2x - 3) + 1(2x - 3)
= (2x - 3)(3x + 1).
∴ 10(6x2 - 7x - 3) = 10(2x - 3)(3x + 1).
Hence, 60x2 - 70x - 30 = 10(2x - 3)(3x + 1).
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