What is ((x^3-2x^2-5x+6))/((x-3)) ?

The solution to ((x^3-2x^2-5x+6))/((x-3)) is (x-1)(x+2)

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simplify ((x^3-2x^2-5x+6))/((x-3))

simplify

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

(x - 1) (x + 2)

Solution steps

\frac{x ^{3} - 2 x ^{2} - 5 x + 6}{x - 3}

Use the rational root theorem

= \frac{( x - 1 ) \frac{x ^{3} - 2 x ^{2} - 5 x + 6}{x - 1}}{x - 3}

\frac{x ^{3} - 2 x ^{2} - 5 x + 6}{x - 1} = x^{2} - x - 6

= \frac{( x - 1 ) ( x ^{2} - x - 6 )}{x - 3}

Factor

x^{2} - x - 6 : (x + 2) (x - 3)

= \frac{( x - 1 ) ( x + 2 ) ( x - 3 )}{x - 3}

Cancel the common factor:

x - 3

= (x - 1) (x + 2)

(x - 1) (x - 2)^{2}

\frac{9 x - 4}{8} + \frac{3 x + 8}{8}

(x + 2)^{2}

\frac{1 + \frac{1}{x - 1}}{1 + \frac{1}{x ^{2} - 1}}

3 x^{4} - 2 x^{4} + 7 x^{4}

What is ((x^3-2x^2-5x+6))/((x-3)) ?
The solution to ((x^3-2x^2-5x+6))/((x-3)) is (x-1)(x+2)