Discrete Math

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Directions: Find the quotient and the remainder when the first polynomial is divided by the second.
#9. 3x^4 – 2x^3 + 5x^2 + x + 1;x^2 + 2x

  • Discrete Math -

    Do exactly as you would do in a long division of numbers:

    3x^4 – 2x^3 + 5x^2 + x + 1;x^2 + 2x

    I will do it below, but the coefficients will not be lined up because I do not know how to insert spaces that don't get merged at this forum.
    Divide x^2+2x into

    3x^4 – 2x^3 + 5x^2 + x + 1

    First divide 3x^4 by x^2 to get 3x^2.

    Then multiply (x^2+2x) by 3x^2 to get
    3x^4+6x^3

    Subtract 3x^4+6x^3 from 3x^4 – 2x^3 + 5x^2 + x + 1 to get
    – 8x^3 + 5x^2 + x + 1

    Repeat the same as above:
    Divide -8x^3 by x^2 to get -8x

    Multiply x^2+2x by -8x to get -8x^3 -16x^2.

    Subtract -8x^3 -16x^2 from – 8x^3 + 5x^2 + x + 1 to get 21x^2 +x + 1.

    The same process will repeat itself to get the final answer by collecting all the above quotient terms:
    3x^2-8x+21 with a remainder of -41x+1

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