Nice Add. Maths. Qn

• wee_ws

  11 May 10, 08:06

  Hi,

    Students can give this question a try:

    When a polynomial h(x) is divided by (x - 1) and (x + 3) the remainder is -2 and 10 respectively. Find the remainder when h(x) is divided by (x - 1)(x + 3).

    Thanks.

  Cheers,
  Wen Shih

• AmuletxHeart

  15 May 10, 15:48

  Ok. Just trying, might not be correct.

  h(1) = -2

  h(-3)= 10

  h(1 times -3)= -2 times 10

                        = -20

• SBS261P

  15 May 10, 21:49

  is the answer 2?

• wee_ws

  16 May 10, 07:25

  Hi,

    The answer is a linear expression.

    Please take note of the following points: 

    1. When a polynomial is divided by a linear factor, the remainder is a constant.

    2. When a polynomial is divided by a quadratic factor, the remainder is a linear expression.

    To convince yourself about point 2, consider (x^3 + 1) / (x^2 - 2x). Thanks.

  Cheers,
  Wen Shih

• wee_ws

  16 May 10, 08:12

  Hi,

    The steps to solving the question are given below as reference:

    Let h(x) / {(x - 1)(x + 3)} = Q(x) + A / (x - 1) + B / (x + 3), where Q(x) is some polynomial.

    Then h(x) = (x - 1)(x + 3)Q(x) + A(x + 3) + B(x -1). Note that the last 2 terms form the remainder of h(x) when it is divided by (x - 1)(x + 3).

    Since h(1) = -2, we can solve for A.

    Since h(-3) = 10, we can find the value of B.

    Thanks.

  Cheers,
  Wen Shih