Factorise : (a2-2a)2-23(a2-2a)+120
(a2 – 2a)2 – 23(a2 – 2a) + 120
Let (a2 – 2a) = x, then given polynomial becomes
x2 – 23x + 120
= x2 – 15x – 8x + 120
= x(x – 15) – 8 (x – 15)
= (x – 15) (x – 8)
On substituting the value of x, we get
(a2 – 2a)2 – 23(a2 – 2a) + 120
= (a2 – 2a – 15) (a2 – 2a – 8)
= (a2 – 5a + 3a – 15) (a2 – 4a + 2a – 8)
= (a – 5) (a + 3) (a – 4) (a + 2)