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Thread: polynomial

  1. #1
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    polynomial

    the polynomial p(x) = $\displaystyle x^4+ax^3-10x^2+bx-12$ is divisible by d(x) = $\displaystyle (x+4)(x-3)$ Calculate the quotient of the division of P(x) of D(x).


    Answer:
    $\displaystyle x^2+x+1$
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  2. #2
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    Quote Originally Posted by Apprentice123 View Post
    the polynomial p(x) = $\displaystyle x^4+ax^3-10x^2+bx-12$ is divisible by d(x) = $\displaystyle (x+4)(x-3)$ Calculate the quotient of the division of P(x) of D(x).


    Answer:
    $\displaystyle x^2+x+1$
    Hi

    Dividing $\displaystyle x^4+ax^3-10x^2+bx-12$ by d(x) = $\displaystyle (x+4)(x-3)$ gives
    $\displaystyle x^2+(a-1)x+3-a$ and a rest $\displaystyle (b+13a-15)x+12 (2-a)$
    The rest is equal to 0 therefore
    a = 2
    b = -11
    Quotient is $\displaystyle x^2+x+1$
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  3. #3
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    Thank you
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