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

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

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

simplify

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

(x + 1) (x + 3)

Solution steps

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

Use the rational root theorem

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

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

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

Factor

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

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

Cancel the common factor:

x - 2

= (x + 1) (x + 3)

(a - 6) (a + 6)

\frac{3}{5} + \frac{2}{4}

a (a + b)

- 1 0^{0}

(3 x - 2 y)^{6}

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