Show that (x-2), (x+3) and (x-4) are factors of x³-3x²-10x+24.

Let, f (x) = x³-3x²-10x+24 be the given polynomial.

In order to prove that (x – 2) (x + 3) (x – 4) are the factors of f (x), it is sufficient to show that f (2) = 0, f (-3) = 0 and f (4) = 0 respectively.

Now,

f (x) = x³-3x²-10x+24

f (2) = (2)³ – 3 (2)² – 10 (2) + 24

= 8 – 12 – 20 + 24

= 0

f (-3) = (-3)³ – 3 (-3)² – 10 (-3) + 24

= -27 – 27 + 30 + 24

= 0

f (4) = (4)³ – 3 (4)² – 10 (4) + 24

= 64 – 48 – 40 + 24

= 0

Hence, (x – 2), (x + 3) and (x – 4) are the factors of the given polynomial.