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Math Help - Algebra

  1. #1
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    Algebra

    When a polynomial is divided by (x+2) the remainder is 19. When the same polynomial is divided by (x-1) the remainder is 2. Determine the remainder when the polynomial is divided by (x-1)(x+2).
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  2. #2
    Super Member Bacterius's Avatar
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    Divide a polynomial ? Wouldn't it be just a number ?
    What type of polynomial is it ? Quadratic, linear, ternary ?
    Is the x stated in your question the same as the unknown of the polynomial ?
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  3. #3
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    Quote Originally Posted by Bacterius View Post
    Divide a polynomial ? Wouldn't it be just a number ?
    What type of polynomial is it ? Quadratic, linear, ternary ?
    Is the x stated in your question the same as the unknown of the polynomial ?
    It doesn't matter the degree of the polynomial, as long as it degree 3 or more it can divide by two factors. When you divide a polynomial by (x-a), the result is another polynomial with degree one less than the previous one and a possible remainder term, unless it divides evenly.

    I've been thinking about this problem and I can't figure it out 100%. I am almost sure you either add them or multiply, but I can't see which one.
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  4. #4
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    Quote Originally Posted by KingV15 View Post
    When a polynomial is divided by (x+2) the remainder is 19. When the same polynomial is divided by (x-1) the remainder is 2. Determine the remainder when the polynomial is divided by (x-1)(x+2).
    HI

    f(1)=2 , f(-2)=19

    Lets assume that the remainder of f(x) is Ax+B . We can make this assumption because :

    When f(x) is divided by (x-1)(x+2) , there is a quotient q(x) and a remainder r(x) .

    f(x)=(x-1)(x+2)q(x)+r(x)

    where r(x)=0 or \deg r(x)<\deg (x-1)(x+2)=2


    so now f(x)=(x-1)(x+2)q(x)+Ax+B
    f(1)=A+B\Rightarrow 2=A+B --- 1

    f(-2)=-2A+B\Rightarrow 19=-2A+B ---- 2

    Solve the simultaneous equations .
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