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)

(y + 3) (y + 1)

3 \div \frac{7}{4}

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

\frac{1}{6} + \frac{5}{3}

0.28

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)