Solve x^3/16+3x/4+81/16

$$\frac { x ^ { 3 } } { 16 } + \frac { 3 x } { 4 } + \frac { 81 } { 16 }$$

Evaluate

$$\frac{x^{3}+12x+81}{16}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 16 and 4 is 16. Multiply \frac{3x}{4} times \frac{4}{4}.

$$\frac{x^{3}}{16}+\frac{4\times 3x}{16}+\frac{81}{16}$$

Since \frac{x^{3}}{16} and \frac{4\times 3x}{16} have the same denominator, add them by adding their numerators.

$$\frac{x^{3}+4\times 3x}{16}+\frac{81}{16}$$

Do the multiplications in x^{3}+4\times 3x.

$$\frac{x^{3}+12x}{16}+\frac{81}{16}$$

Since \frac{x^{3}+12x}{16} and \frac{81}{16} have the same denominator, add them by adding their numerators.

$$\frac{x^{3}+12x+81}{16}$$

Factor

$$\frac{x^{3}+12x+81}{16}$$

Solution Steps

Factor out \frac{1}{16}. Polynomial x^{3}+12x+81 is not factored since it does not have any rational roots.

$$\frac{x^{3}+12x+81}{16}$$