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Perform the following polynomials divisions: (12 marks)

(x2 - 7x - 12) ÷ (x + 2)
(x3 + x2 – 3x + 1) ÷ (x – 1)
(3x3 + 5x2 – 3x – 5) ÷ (x + 1)
(x4 - 3x3 + 3x + 2) ÷ (x - 2)

Based on the results of question 1, what do you notice when the divisor is a factor of the polynomial? (1 mark)

  • math -

    correction

    (x^2 - 7x - 12) ÷ (x + 2)
    (x^3 + x^2 – 3x + 1) ÷ (x – 1)
    (3x^3 + 5x^2 – 3x – 5) ÷ (x + 1)
    (x^4 - 3x^3 + 3x + 2) ÷ (x - 2)

  • math -

    (x^2 - 7x - 12) ÷ (x + 2) = (x-9) remainder 6

    (x^3 + x^2 – 3x + 1) ÷ (x – 1) = (x^2+2x-1) remainder 0

    (3x^3 + 5x^2 – 3x – 5) ÷ (x + 1) = 3x^2+2x-5 remainder 0

    (x^4 - 3x^3 + 3x + 2) ÷ (x - 2) = x^3-x^2-2x-1 remainder 0

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