How do you simplify and divide $\frac{x^{3} - 4 x^{2} + 5 x - 6}{x^{2} - x + 2}$ $(x^3-4x^2+5x-6)/(x^2-x+2)$ ?

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Answer 1 · 2017-07-24T11:49:23

$(x - 3)$ $(x-3)$

$\frac{x^{3} - 4 x^{2} + 5 x - 6}{x^{2} - x + 2}$ $(x^3 -4x^2 +5x -6 )/(x^2-x+2)$

$= \frac{x^{3} - 3 x^{2} - x^{2} + 3 x + 2 x - 6}{x^{2} - x + 2}$ $= (x^3- 3x^2 -x^2+3x +2x -6 )/(x^2-x+2)$

$= \frac{x^{2} (x - 3) - x (x - 3) + 2 (x - 3)}{x^{2} - x + 2}$ $= (x^2(x- 3) -x(x-3) +2(x -3 ))/(x^2-x+2)$

$= ((x- 3) cancel((x^2-x+2)))/cancel((x^2-x+2) )$

$= (x-3)$ [Ans]

How do you simplify and divide (x^3-4x^2+5x-6)/(x^2-x+2)x3−4x2+5x−6x2−x+2(x^3-4x^2+5x-6)/(x^2-x+2)?