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Math Help - Polynomials

  1. #1
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    Polynomials

    1, Find the values of a and b so that the polynomials x^3 + ax^2 + bx + 6 has x -2 as a factor and leaves a reminder 3 when divided by x-3

    2, If ax^3 + bx^2 + x -b has x+2 as a factor and leaves a reminder 4 when divided by x-2 , find the values of a and b
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  2. #2
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    Re: Polynomials

    These are applications of the remainder and factor theorems. If a polynomial $\displaystyle \begin{align*} P(x) \end{align*}$ is divided by $\displaystyle \begin{align*} (x - \alpha ) \end{align*}$, then the remainder is equal to $\displaystyle \begin{align*} P \left( \alpha \right) \end{align*}$.
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