Multiple Choice Question (MCQ)

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 ?

  1. ×

    4

  2. ×

    6

  3. 10

  4. ×

    12

  5. ×

    14

Collected in the board: Algebraic equation

Steven Zheng posted 2 months ago


Answer

  1. 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

Steven Zheng posted 2 months ago

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