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Section 5-1 : Dividing Polynomials

4. Use synthetic division to divide \({x^3} + {x^2} + x + 1\) by \(x + 9\).

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Here is the synthetic division. We’ll leave it to you to check all the numbers.

\[\begin{array}{*{20}{r}}{\left. {\underline {\,{ - 9} \,}}\! \right| }\\{}\\{}\end{array}\,\,\,\,\begin{array}{*{20}{r}}1&1&1&1\\{}&{ - 9}&{72}&{ - 657}\\\hline1&{ - 8}&{73}&{ - 656}\end{array}\] Show Step 2

The answer is then,

\[{x^3} + {x^2} + x + 1 = \left( {x + 9} \right)\left( {{x^2} - 8x + 73} \right) - 656\]

Note that we only gave one form of the answer (unlike the first couple of problems) since this is often the form we need when using synthetic division and it is also the form that method is set up to give.