Solve f(x)=27x^3+1/3x^2+sqrt{8x}

$$f ( x ) = 27 x ^ { 3 } + \frac { 1 } { 3 } x ^ { 2 } + \sqrt { 8 x }$$

Factor

$$\frac{\sqrt{x}\left(81x^{\frac{5}{2}}+x^{\frac{3}{2}}+6\sqrt{2}\right)}{3}$$

Solution Steps

Factor out \frac{1}{3}.

$$\frac{81x^{3}+x^{2}+6\sqrt{2}\sqrt{x}}{3}$$

Consider 81x^{3}+x^{2}+3\sqrt{8}\sqrt{x}. Factor out \sqrt{x}.

$$\sqrt{x}\left(81x^{\frac{5}{2}}+x^{\frac{3}{2}}+6\sqrt{2}\right)$$

Rewrite the complete factored expression.

$$\frac{\sqrt{x}\left(81x^{\frac{5}{2}}+x^{\frac{3}{2}}+6\sqrt{2}\right)}{3}$$

Evaluate

$$27x^{3}+\frac{x^{2}}{3}+2\sqrt{2x}$$