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

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

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simplify ((x^3+2x^2-5x-6))/((x+1))

simplify

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

(x - 2) (x + 3)

Solution steps

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

Use the rational root theorem

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

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

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

Factor

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

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

Cancel the common factor:

x + 1

= (x - 2) (x + 3)

6 x^{2} - 13 x + 7

\frac{( 3 - i )}{4 + 2 i}

\frac{45}{24}

\frac{\frac{3}{2}}{( - \frac{\frac{2}{3}}{\frac{4}{12}} )}

2 (5 + 2)

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