Solve 15x^3-14x^2-8xdiv5x+2

$$15 { x }^{ 3 } -14 { x }^{ 2 } -8x \div 5x+2$$

Evaluate

$$15x^{3}-\frac{78x^{2}}{5}+2$$

Short Solution Steps

Express \frac{8x}{5}x as a single fraction.

$$15x^{3}-14x^{2}-\frac{8xx}{5}+2$$

Multiply x and x to get x^{2}.

$$15x^{3}-14x^{2}-\frac{8x^{2}}{5}+2$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 15x^{3}-14x^{2} times \frac{5}{5}.

$$\frac{5\left(15x^{3}-14x^{2}\right)}{5}-\frac{8x^{2}}{5}+2$$

Since \frac{5\left(15x^{3}-14x^{2}\right)}{5} and \frac{8x^{2}}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5\left(15x^{3}-14x^{2}\right)-8x^{2}}{5}+2$$

Do the multiplications in 5\left(15x^{3}-14x^{2}\right)-8x^{2}.

$$\frac{75x^{3}-70x^{2}-8x^{2}}{5}+2$$

Combine like terms in 75x^{3}-70x^{2}-8x^{2}.

$$\frac{75x^{3}-78x^{2}}{5}+2$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{5}{5}.

$$\frac{75x^{3}-78x^{2}}{5}+\frac{2\times 5}{5}$$

Since \frac{75x^{3}-78x^{2}}{5} and \frac{2\times 5}{5} have the same denominator, add them by adding their numerators.

$$\frac{75x^{3}-78x^{2}+2\times 5}{5}$$

Do the multiplications in 75x^{3}-78x^{2}+2\times 5.

$$\frac{75x^{3}-78x^{2}+10}{5}$$

Factor

$$\frac{75x^{3}-78x^{2}+10}{5}$$

Solution Steps

Factor out \frac{1}{5}. Polynomial 75x^{3}-78x^{2}+10 is not factored since it does not have any rational roots.

$$\frac{75x^{3}-70x^{2}-8xx+10}{5}$$