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Math Help - remainders

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    remainders

    when 3x^3 + 2x^2 + ax +b is divided by x-1 the remainder is 5. when divided by 3x-1 the remainder is -1/3. find values of a and b

    thanks everyone
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    Quote Originally Posted by gracey View Post
    when 3x^3 + 2x^2 + ax +b is divided by x-1 the remainder is 5. when divided by 3x-1 the remainder is -1/3. find values of a and b

    thanks everyone
    Use the remainder theorem:

    When a polynomial P(x) is divided by (\alpha x - \beta) the remainder is P\left( \frac{\beta}{\alpha}\right).

    Let P(x) = 3x^3 + 2x^2 + ax + b. Then:


    P(1) = 5 \Rightarrow 3 + 2 + a + b = 5 \Rightarrow a + b = 0 .... (1)


    P\left( \frac{1}{3}\right) = - \frac{1}{3} \Rightarrow .... .... (2)


    Solve equations (1) and (2) simultaneously for a and b.
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