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

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

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

simplify

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

x^{2} + 3 x + 1

Solution steps

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

Factor

x^{3} + x^{2} - 5 x - 2 : (x - 2) (x^{2} + 3 x + 1)

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

Cancel the common factor:

x - 2

= x^{2} + 3 x + 1

\frac{1}{5} \div \frac{2}{3}

\frac{( x ^{2} + 7 x + 12 )}{( x + 4 )}

b^{2} + 8 b + 15

\frac{x y - x}{2 ( y - 1 )}

\frac{x ^{5} + 32}{x + 2}