Use synthetic division method for performing the following division. Write the result in the form
Dividend = Divisor x Quotient + Remainder.

$(x^{3} - 3 x^{2} - 12 x + 4) \div (x - 2)$

(x - 2) (x^{2} - x - 14) - 24

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(x + 2) (x^{2} - x - 9) - 7

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(x + 4) (x^{2} - x - 1) - 4

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(x + 7) (x^{2} - x - 4) - 12

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Solution

The correct option is A $(x - 2) (x^{2} - x - 14) - 24$
Therefore,
Quotient= $x^{2} - x - 14$
Remainder= $- 24$
Therefore,
$x^{3} - 3 x^{2} - 12 x + 4 = (x - 2) (x^{2} - x - 14) - 24$

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