Final answer to the problem
$4x^{2}+4x-3+\frac{27}{x-1}$
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Step-by-step Solution
How should I solve this problem?
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- Write in simplest form
- Solve by quadratic formula (general formula)
- Find the derivative using the definition
- Simplify
- Find the integral
- Find the derivative
- Factor
- Factor by completing the square
- Find the roots
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1
Divide $4x^3-7x+30$ by $x-1$
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-1;}{\phantom{;}4x^{2}+4x\phantom{;}-3\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-1\overline{\smash{)}\phantom{;}4x^{3}\phantom{-;x^n}-7x\phantom{;}+30\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-1;}\underline{-4x^{3}+4x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-4x^{3}+4x^{2};}\phantom{;}4x^{2}-7x\phantom{;}+30\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-1-;x^n;}\underline{-4x^{2}+4x\phantom{;}\phantom{-;x^n}}\\\phantom{;-4x^{2}+4x\phantom{;}-;x^n;}-3x\phantom{;}+30\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-1-;x^n-;x^n;}\underline{\phantom{;}3x\phantom{;}-3\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}3x\phantom{;}-3\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}27\phantom{;}\phantom{;}\\\end{array}$
2
Resulting polynomial
$4x^{2}+4x-3+\frac{27}{x-1}$
Final answer to the problem
$4x^{2}+4x-3+\frac{27}{x-1}$
