Mathematics
Factorise the following:
a2 - 3a - 54
Factorisation
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Answer
To factorise a2 - 3a - 54, we want to find two real numbers whose sum is -3 and product is -54. By trial, we see that -9 + 6 = -3 and -9 × 6 = -54.
∴ a2 - 3a - 54 = a2 - 9a + 6a - 54
= a(a - 9) + 6(a - 9)
= (a - 9)(a + 6).
Hence, a2 - 3a - 54 = (a - 9)(a + 6).
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