If a remainder of $$ 4 $$ is obtained when $$ x^3+2x^2-x-k $$ is devided by $$ x-2 $$ , what is the value of $$ k $$ ?

Question

Uniteasy Admin · Accepted Answer

Using long division for the polynomial
$$ x-2)\overline{x^3+2x^2-x-k}$$
$$\qquad \enspace \,\underline{x^3-2x^2}$$
$$\qquad\qquad  \enspace \,4x^2-x$$
$$\qquad\qquad  \enspace \,\underline{4x^2-8x}$$ 
$$\qquad\qquad\qquad \enspace\,\,\,\, \,7x-k$$
$$\qquad\qquad\qquad \enspace\,\,\,\, \,\underline{7x-14}$$
$$\qquad\qquad\qquad\qquad \enspace\,\,\,\, \,-k+14$$ 
Since the remainder is equal to 4,
$$-k+14 =4$$
Therefore, 
$$k=10$$

C is the choice

Multiple Choice Question (MCQ)

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