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Polynomial Division Practice Problems

based on 2 ratings
By — McGraw-Hill Professional
Updated on Oct 4, 2011

To review these concepts, go to Polynomial Division Help and Synthetic Division Help

Polynomial Division Practice Problems

Problems

For Problems 1-4 use long division to find the quotient and remainder. For Problems 5 and 6, use synthetic division

  1. (6 x 3 − 2 x 2 + 5 x − 1) ÷ ( x 2 + 3 x + 2)

  2. ( x 3x 2 + 2 x + 5) ÷ (3 x − 4)

Polynomial Functions Practice

  1. ( x 3 + 8) ÷ ( x + 2)

  2. Use synthetic division and the Remainder Theorem to evaluate f(c) .

    f(x) = 6 x 4 − 8 x 3 + x 2 + 2 x − 5; c = −2

  3. Completely factor the polynomial. f(x) = x 3 + 2 x 2x − 2; c = 1 is a zero.

  4. Completely factor the polynomial. P(x) = x 3 − 5 x 2 + 5 x + 3; c = 3 is a zero.

Solutions

  1.  

    Polynomial Functions Solutions

    The quotient is 6 x − 20, and the remainder is 53 x + 39.

  2.  

    Polynomial Functions Solutions

  3.  

    Polynomial Functions Solutions

     

    Polynomial Functions Solutions

    The quotient is −6 x + 2, and the remainder is 10 x .

  4.  

    Polynomial Functions Solutions

    The quotient is x 2 + x + 1, and the remainder is 0.

  5.  

    Polynomial Functions Solutions

    The quotient is x 2x + 4, and the remainder is −20.

  6.  

    Polynomial Functions Solutions

    The quotient is x 2 − 2 x + 4, and the remainder is 0.

  7.  

    Polynomial Functions Solutions

    The remainder is 155, so f (−2) = 155.

  8.  

    Polynomial Functions Solutions

    f(x) = ( x − 1)( x 2 + 3 x + 2)

    = ( x − 1)( x + 1)( x + 2)

  9.  

    Polynomial Functions Solutions

    P(x) = ( x − 3)( x 2 − 2 x − 1)

    In order to factor x 2 − 2 x − 1, we must first find its zeros.

    Polynomial Functions Solutions

    Because Polynomial Functions Solutions is a zero, Polynomial Functions Solutions = Polynomial Functions Solutions is a factor.

    Because Polynomial Functions Solutions is a zero, Polynomial Functions Solutions = Polynomial Functions Solutions is a factor.

    Polynomial Functions Solutions

 

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