By actual division, show that x3 – 3 is a factor 2x4 + 3x3 – 2x2 – 9x – 12.
It is given in the question that,
f (x) = 2x4 + 3x3 – 2x2 – 9x – 12
And, g (x) = x3 – 3
Hence,
Quotient q (x) = 2x2 + 3x + 4
Remainder r (x) = 0
As the remainder is 0
∴ x2 – 3 is a factor of 2x4 + 3x3 – 2x2 – 9x – 12
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