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    The question is as follows:
    Find the values of c and d so that 2x^3 + 5x^2 + cx + d is exactly divisible by (x - 2)(x + 3).

    Worked solution:
    (x - 2)(x + 3) = x^2 + 3x - 2x - 6 = x^2 + x - 6
    2x (x^2 + x - 6) = 2x^3 + 2x^2 - 12x
    3 (x^2 + x - 6) = 3x^2 + 3x - 18
    2x^3 + 5x^2 - 9x - 18

    Hence, c = -9, d = -18.

    This is the correct answer, however the book uses a different method to find the answer.

    Textbook solution:
    f(2) = ....
    f(-3) = ...
    Combination of f(2) and f(-3).
    Hence, gives c = -9, d = -18.
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    (Original post by Dooderman)
    The question is as follows:
    Find the values of c and d so that 2x^3 + 5x^2 + cx + d is exactly divisible by (x - 2)(x + 3).

    Worked solution:
    (x - 2)(x + 3) = x^2 + 3x - 2x - 6 = x^2 + x - 6
    2x (x^2 + x - 6) = 2x^3 + 2x^2 - 12x
    3 (x^2 + x - 6) = 3x^2 + 3x - 18
    2x^3 + 5x^2 - 9x - 18

    Hence, c = -9, d = -18.

    This is the correct answer, however the book uses a different method to find the answer.

    Textbook solution:
    f(2) = ....
    f(-3) = ...
    Combination of f(2) and f(-3).
    Hence, gives c = -9, d = -18.
    You should get the marks. (but your way relies on quite a bit of guessing and trial-and-error, I'd suggest learning the intended method; it's a lot more systematic)
 
 
 
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