Q9 of 113 Page 60

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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