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### Section 5-1 : Dividing Polynomials

6. Use synthetic division to divide $$5{x^4} + {x^2} - 8x + 2$$ by $$x - 4$$.

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

$\begin{array}{*{20}{r}}{\left. {\underline {\,4 \,}}\! \right| }\\{}\\{}\end{array}\,\,\,\,\begin{array}{*{20}{r}}5&0&1&{ - 8}&2\\{}&{20}&{80}&{324}&{1264}\\\hline5&{20}&{81}&{316}&{1266}\end{array}$ Show Step 2

$5{x^4} + {x^2} - 8x + 2 = \left( {x - 4} \right)\left( {5{x^3} + 20{x^2} + 81x + 316} \right) + 1266$