Exercise
$\frac{-2x^3-3x^2+6x-4}{x^2-x+1}$
Step-by-step Solution
1
Divide $-2x^3-3x^2+6x-4$ by $x^2-x+1$
$\begin{array}{l}\phantom{\phantom{;}x^{2}-x\phantom{;}+1;}{-2x\phantom{;}-5\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-x\phantom{;}+1\overline{\smash{)}-2x^{3}-3x^{2}+6x\phantom{;}-4\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-x\phantom{;}+1;}\underline{\phantom{;}2x^{3}-2x^{2}+2x\phantom{;}\phantom{-;x^n}}\\\phantom{\phantom{;}2x^{3}-2x^{2}+2x\phantom{;};}-5x^{2}+8x\phantom{;}-4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-x\phantom{;}+1-;x^n;}\underline{\phantom{;}5x^{2}-5x\phantom{;}+5\phantom{;}\phantom{;}}\\\phantom{;\phantom{;}5x^{2}-5x\phantom{;}+5\phantom{;}\phantom{;}-;x^n;}\phantom{;}3x\phantom{;}+1\phantom{;}\phantom{;}\\\end{array}$
$-2x-5+\frac{3x+1}{x^2-x+1}$
Final answer to the exercise
$-2x-5+\frac{3x+1}{x^2-x+1}$