Solve (x^3+3x^2-2x-14)divsqrt{2}

$$( { x }^{ 3 } +3 { x }^{ 2 } -2x-14) \div \sqrt{ 2 }$$

Evaluate

$$\frac{\sqrt{2}\left(x^{3}+3x^{2}-2x-14\right)}{2}$$

Solution Steps

Rationalize the denominator of \frac{x^{3}+3x^{2}-2x-14}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\left(x^{3}+3x^{2}-2x-14\right)\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\left(x^{3}+3x^{2}-2x-14\right)\sqrt{2}}{2}$$

Use the distributive property to multiply x^{3}+3x^{2}-2x-14 by \sqrt{2}.

$$\frac{x^{3}\sqrt{2}+3x^{2}\sqrt{2}-2x\sqrt{2}-14\sqrt{2}}{2}$$

Differentiate w.r.t. x

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