Final Answer
$x^{3}+5x^{2}+24x+121+\frac{602}{x-5}$
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Step-by-step Solution
Specify the solving method
1
Divide $x^4-x^2+x-3$ by $x-5$
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-5;}{\phantom{;}x^{3}+5x^{2}+24x\phantom{;}+121\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-5\overline{\smash{)}\phantom{;}x^{4}\phantom{-;x^n}-x^{2}+x\phantom{;}-3\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-5;}\underline{-x^{4}+5x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}+5x^{3};}\phantom{;}5x^{3}-x^{2}+x\phantom{;}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-5-;x^n;}\underline{-5x^{3}+25x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-5x^{3}+25x^{2}-;x^n;}\phantom{;}24x^{2}+x\phantom{;}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-5-;x^n-;x^n;}\underline{-24x^{2}+120x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-24x^{2}+120x\phantom{;}-;x^n-;x^n;}\phantom{;}121x\phantom{;}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-5-;x^n-;x^n-;x^n;}\underline{-121x\phantom{;}+605\phantom{;}\phantom{;}}\\\phantom{;;;-121x\phantom{;}+605\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}602\phantom{;}\phantom{;}\\\end{array}$
2
Resulting polynomial
$x^{3}+5x^{2}+24x+121+\frac{602}{x-5}$
Final Answer
$x^{3}+5x^{2}+24x+121+\frac{602}{x-5}$