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Perform polynomial long division for the following: 1. x2 - 9x - 10 divided by x + 1. 2. 2x3 - 9x2 + 15 divided by 2x - 5. Write answers in the form dividenddivisor = quotient + remainderdivisor.

Mathematics

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Here are the solutions using long division, with each answer written in the form dividenddivisor=quotient+remainderdivisor\frac{\text{dividend}}{\text{divisor}} = \text{quotient} + \frac{\text{remainder}}{\text{divisor}}.

1. x2−9x−10x^2 - 9x - 10 divided by x+1x + 1.

  1. Set up the long division.

    x−10x+1)x2−9x−10‾\begin{array}{r} x - 10 \\ x+1 \overline{) x^2 - 9x - 10} \\ \end{array}

  2. Perform the long division.

    x−10x+1)x2−9x−10‾−(x2+x)−10x−10−(−10x−10)0\begin{array}{r} x - 10 \\ x+1 \overline{) x^2 - 9x - 10} \\ - (x^2 + x) \\ \hline -10x - 10 \\ - (-10x - 10) \\ \hline 0 \end{array}

  3. Identify the quotient and remainder.

    The quotient is x−10x - 10.
    The remainder is 0.

  4. Write the answer in the specified form.

    x2−9x−10x+1=x−10+0x+1\boxed{\frac{x^2 - 9x - 10}{x + 1} = x - 10 + \frac{0}{x + 1}}

    2. 2x3−9x2+152x^3 - 9x^2 + 15 divided by 2x−52x - 5.

  5. Set up the long division

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