What is (x^3+5x^2-17x-21)/((x+1)) ?

The solution to (x^3+5x^2-17x-21)/((x+1)) is (x-3)(x+7)

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simplify (x^3+5x^2-17x-21)/((x+1))

simplify

\frac{x ^{3} + 5 x ^{2} - 17 x - 21}{( x + 1 )}

(x - 3) (x + 7)

Solution steps

\frac{x ^{3} + 5 x ^{2} - 17 x - 21}{x + 1}

Use the rational root theorem

= \frac{( x + 1 ) \frac{x ^{3} + 5 x ^{2} - 17 x - 21}{x + 1}}{x + 1}

\frac{x ^{3} + 5 x ^{2} - 17 x - 21}{x + 1} = x^{2} + 4 x - 21

= \frac{( x + 1 ) ( x ^{2} + 4 x - 21 )}{x + 1}

Factor

x^{2} + 4 x - 21 : (x - 3) (x + 7)

= \frac{( x + 1 ) ( x - 3 ) ( x + 7 )}{x + 1}

Cancel the common factor:

x + 1

= (x - 3) (x + 7)

(x^{2} + 4) (x^{2} - 6)

(- 3 x^{2} + 9 x - 9) + (- 9 x^{2} + 9 x + 3)

\frac{5 ^{7}}{5 ^{3}}

- 1 + (- 3)

lo g_{4} (10)

What is (x^3+5x^2-17x-21)/((x+1)) ?
The solution to (x^3+5x^2-17x-21)/((x+1)) is (x-3)(x+7)