Answer :
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.
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