Solve 4x^2-frac{sqrt{3}}{3}x+16/3

$$4 x ^ { 2 } - \frac { \sqrt { 3 } } { 3 } x + \frac { 16 } { 3 }$$

Evaluate

$$4x^{2}-\frac{\sqrt{3}x}{3}+\frac{16}{3}$$

Short Solution Steps

Express \frac{\sqrt{3}}{3}x as a single fraction.

$$4x^{2}-\frac{\sqrt{3}x}{3}+\frac{16}{3}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4x^{2} times \frac{3}{3}.

$$\frac{3\times 4x^{2}}{3}-\frac{\sqrt{3}x}{3}+\frac{16}{3}$$

Since \frac{3\times 4x^{2}}{3} and \frac{\sqrt{3}x}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\times 4x^{2}-\sqrt{3}x}{3}+\frac{16}{3}$$

Do the multiplications in 3\times 4x^{2}-\sqrt{3}x.

$$\frac{12x^{2}-\sqrt{3}x}{3}+\frac{16}{3}$$

Since \frac{12x^{2}-\sqrt{3}x}{3} and \frac{16}{3} have the same denominator, add them by adding their numerators.

$$\frac{12x^{2}-\sqrt{3}x+16}{3}$$

Factor

$$\frac{12x^{2}-\sqrt{3}x+16}{3}$$

Solution Steps

Factor out \frac{1}{3}. Polynomial 12x^{2}-\sqrt{3}x+16 is not factored since it does not have any rational roots.

$$\frac{12x^{2}-\sqrt{3}x+16}{3}$$