Exercise
$\frac{12x^4-36x^6-29x^2+38x+24}{2x^2-5x-6}$
Step-by-step Solution
1
Divide $12x^4-36x^6-29x^2+38x+24$ by $2x^2-5x-6$
$\begin{array}{l}\phantom{\phantom{;}2x^{2}-5x\phantom{;}-6;}{-18x^{4}-45x^{3}-\frac{321}{2}x^{2}+\frac{-\frac{2145}{2}}{2}x\phantom{;}+\frac{-\frac{14693}{4}}{2}\phantom{;}\phantom{;}}\\\phantom{;}2x^{2}-5x\phantom{;}-6\overline{\smash{)}-36x^{6}\phantom{-;x^n}+12x^{4}\phantom{-;x^n}-29x^{2}+38x\phantom{;}+24\phantom{;}\phantom{;}}\\\phantom{\phantom{;}2x^{2}-5x\phantom{;}-6;}\underline{\phantom{;}36x^{6}-90x^{5}-108x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{\phantom{;}36x^{6}-90x^{5}-108x^{4};}-90x^{5}-96x^{4}\phantom{-;x^n}-29x^{2}+38x\phantom{;}+24\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x^{2}-5x\phantom{;}-6-;x^n;}\underline{\phantom{;}90x^{5}-225x^{4}-270x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}90x^{5}-225x^{4}-270x^{3}-;x^n;}-321x^{4}-270x^{3}-29x^{2}+38x\phantom{;}+24\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x^{2}-5x\phantom{;}-6-;x^n-;x^n;}\underline{\phantom{;}321x^{4}-\frac{1605}{2}x^{3}-963x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;\phantom{;}321x^{4}-\frac{1605}{2}x^{3}-963x^{2}-;x^n-;x^n;}-\frac{2145}{2}x^{3}-992x^{2}+38x\phantom{;}+24\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x^{2}-5x\phantom{;}-6-;x^n-;x^n-;x^n;}\underline{\phantom{;}1072.5x^{3}-\frac{10725}{4}x^{2}-3217.5x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;\phantom{;}1072.5x^{3}-\frac{10725}{4}x^{2}-3217.5x\phantom{;}-;x^n-;x^n-;x^n;}-\frac{14693}{4}x^{2}-3179.5x\phantom{;}+24\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x^{2}-5x\phantom{;}-6-;x^n-;x^n-;x^n-;x^n;}\underline{\phantom{;}3673.25x^{2}-\frac{73465}{8}x\phantom{;}-11019.75\phantom{;}\phantom{;}}\\\phantom{;;;;\phantom{;}3673.25x^{2}-\frac{73465}{8}x\phantom{;}-11019.75\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n;}-\frac{98901}{8}x\phantom{;}-10995.75\phantom{;}\phantom{;}\\\end{array}$
$-18x^{4}-45x^{3}-\frac{321}{2}x^{2}-\frac{2145}{4}x-\frac{14693}{8}+\frac{-\frac{98901}{8}x-10995.75}{2x^2-5x-6}$
Final answer to the exercise
$-18x^{4}-45x^{3}-\frac{321}{2}x^{2}-\frac{2145}{4}x-\frac{14693}{8}+\frac{-\frac{98901}{8}x-10995.75}{2x^2-5x-6}$