What is (x^3+2x^2+5x+10)/(x^2+4x+4) ?

The solution to (x^3+2x^2+5x+10)/(x^2+4x+4) is (x^2+5)/(x+2)

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simplify (x^3+2x^2+5x+10)/(x^2+4x+4)

simplify

\frac{x ^{3} + 2 x ^{2} + 5 x + 10}{x ^{2} + 4 x + 4}

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

Solution steps

\frac{x ^{3} + 2 x ^{2} + 5 x + 10}{x ^{2} + 4 x + 4}

Factor

x^{3} + 2 x^{2} + 5 x + 10 : (x + 2) (x^{2} + 5)

= \frac{( x + 2 ) ( x ^{2} + 5 )}{x ^{2} + 4 x + 4}

Factor

x^{2} + 4 x + 4 : (x + 2)^{2}

= \frac{( x + 2 ) ( x ^{2} + 5 )}{( x + 2 ) ^{2}}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(x + 2)^{2} = (x + 2) (x + 2)

= \frac{( x + 2 ) ( x ^{2} + 5 )}{( x + 2 ) ( x + 2 )}

Cancel the common factor:

x + 2

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

3 x^{108} + 3 x^{108}

(- 6 x^{3} + 2)^{4}

\frac{( 2 x - 4 )}{( x ^{2} - 4 )}

(5 z^{- 3} \cdot y^{3} \cdot z^{- 7})^{- 1}

56 x + 337 x + 6

What is (x^3+2x^2+5x+10)/(x^2+4x+4) ?
The solution to (x^3+2x^2+5x+10)/(x^2+4x+4) is (x^2+5)/(x+2)