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Math Help - please help! remainder theorems and long division

  1. #1
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    please help! remainder theorems and long division

    When 2x^3 + ax^2 + x + 1 is divided by x + 2 the remainder is -29. Find a.
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  2. #2
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    Quote Originally Posted by greghunter View Post
    When 2x^3 + ax^2 + x + 1 is divided by x + 2 the remainder is -29. Find a.
    When we divide this (is that what you are having trouble with?) we get the remainder to be \frac{4a-17}{x+2}. So solving 4a-17=-29 gives a=-3
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  3. #3
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    Use the remainder theorem, Polynomial remainder theorem - Wikipedia, the free encyclopedia
    Let f(x) = 2x^{3} + ax^{2} + x + 1.

    When f(x) is divided by x + 2 the remainder is -29. Thus the remainder theorem says that f(-2) = -29.

    Hence
    f(-2)=2(-2)^{3} + a(-2)^{2}+(-2)+1=4a-17=-29

    4a-17=-29

    a=-3.
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  4. #4
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    Quote Originally Posted by greghunter View Post
    When 2x^3 + ax^2 + x + 1 is divided by x + 2 the remainder is -29. Find a.
    When the polynomial p(x) is divided by \alpha x - \beta the remainder is p\left( \frac{\beta}{\alpha}\right).

    Therefore p(-2) = 2(-2)^3 + a(-2)^2 + (-2) + 1 = -29. Solve for a.
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