Final Answer
$x^{2}-6x+74+\frac{-563}{x+7}$
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Step-by-step Solution
Specify the solving method
1
Divide $x^3+x^2+32x-45$ by $x+7$
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+7;}{\phantom{;}x^{2}-6x\phantom{;}+74\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+7\overline{\smash{)}\phantom{;}x^{3}+x^{2}+32x\phantom{;}-45\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+7;}\underline{-x^{3}-7x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{3}-7x^{2};}-6x^{2}+32x\phantom{;}-45\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+7-;x^n;}\underline{\phantom{;}6x^{2}+42x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}6x^{2}+42x\phantom{;}-;x^n;}\phantom{;}74x\phantom{;}-45\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+7-;x^n-;x^n;}\underline{-74x\phantom{;}-518\phantom{;}\phantom{;}}\\\phantom{;;-74x\phantom{;}-518\phantom{;}\phantom{;}-;x^n-;x^n;}-563\phantom{;}\phantom{;}\\\end{array}$
2
Resulting polynomial
$x^{2}-6x+74+\frac{-563}{x+7}$
Final Answer
$x^{2}-6x+74+\frac{-563}{x+7}$