Solve f(x)=x^3+2x^2/7+x/8

$$f ( x ) = x ^ { 3 } + \frac { 2 x ^ { 2 } } { 7 } + \frac { x } { 8 }$$

Evaluate

$$x^{3}+\frac{2x^{2}}{7}+\frac{x}{8}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{3} times \frac{7}{7}.

$$\frac{7x^{3}}{7}+\frac{2x^{2}}{7}+\frac{x}{8}$$

Since \frac{7x^{3}}{7} and \frac{2x^{2}}{7} have the same denominator, add them by adding their numerators.

$$\frac{7x^{3}+2x^{2}}{7}+\frac{x}{8}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 7 and 8 is 56. Multiply \frac{7x^{3}+2x^{2}}{7} times \frac{8}{8}. Multiply \frac{x}{8} times \frac{7}{7}.

$$\frac{8\left(7x^{3}+2x^{2}\right)}{56}+\frac{7x}{56}$$

Since \frac{8\left(7x^{3}+2x^{2}\right)}{56} and \frac{7x}{56} have the same denominator, add them by adding their numerators.

$$\frac{8\left(7x^{3}+2x^{2}\right)+7x}{56}$$

Do the multiplications in 8\left(7x^{3}+2x^{2}\right)+7x.

$$\frac{56x^{3}+16x^{2}+7x}{56}$$

Factor

$$\frac{x\left(56x^{2}+16x+7\right)}{56}$$

Solution Steps

Factor out \frac{1}{56}.

$$\frac{56x^{3}+16x^{2}+7x}{56}$$

Consider 56x^{3}+16x^{2}+7x. Factor out x.

$$x\left(56x^{2}+16x+7\right)$$

Rewrite the complete factored expression. Polynomial 56x^{2}+16x+7 is not factored since it does not have any rational roots.

$$\frac{x\left(56x^{2}+16x+7\right)}{56}$$