Answer with Step-by-step explanation:
We have to find the least common multiple of x² – 8x + 12 and x² – x – 2.
on factoring both the terms separately:
x² – 8x + 12
=x²-6x-2x+12
=x(x-6)-2(x-6)
= (x-2)(x-6)
x² – x – 2
=x²-2x+x-2
=x(x-2)+1(x-2)
= (x-2)(x+1)
The factor (x-2) is common between them so we take it once
∴ LCM = (x-2)(x-6)(x+1)
Hence, least common multiple of x² – 8x + 12 and x² – x – 2 is:
(x-2)(x-6)(x+1)
