$Divide 2 x^{3} + x^{2} - 3 x - 3 by 2 x - 1 and verify your answer.$

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Solution

$Quotient = x^{2} + x - 1$
Remainder = -4

VERIFICATION:
$Dividend = Divisor \times Quotient + Remainder$
$∴ Divisor \times Quotient = (2 x - 1) \times (x^{2} + x - 1) + (- 4)$
$= 2 x^{3} + x^{2} - 3 x + 1 + (- 4)$
$= 2 x^{3} + x^{2} - 3 x - 3.$
Hence, the answer is correct.

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