Mathematics
Factorise the following:
a3 - a - 120
Factorisation
27 Likes
Answer
a3 - a - 120 = a3 - a - 125 + 5.
Rearranging above terms we get,
a3 - 125 - a + 5
= [a3 - (5)3] - (a - 5)
We know that,
a3 - b3 = (a - b)(a2 + ab + b2).
[a3 - (5)3] - (a - 5) = (a - 5)(a2 + 5a + 52) - (a - 5)
= (a - 5)(a2 + 5a + 25 - 1)
= (a - 5)(a2 + 5a + 24).
Hence, a3 - a - 120 = (a - 5)(a2 + 5a + 24).
Answered By
10 Likes