Solve x^5/3-9x^2/2+7x-4

$$\frac { x ^ { 5 } } { 3 } - \frac { 9 x ^ { 2 } } { 2 } + 7 x - 4$$

Evaluate

$$\frac{x^{5}}{3}-\frac{9x^{2}}{2}+7x-4$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 2 is 6. Multiply \frac{x^{5}}{3} times \frac{2}{2}. Multiply \frac{9x^{2}}{2} times \frac{3}{3}.

$$\frac{2x^{5}}{6}-\frac{3\times 9x^{2}}{6}+7x-4$$

Since \frac{2x^{5}}{6} and \frac{3\times 9x^{2}}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2x^{5}-3\times 9x^{2}}{6}+7x-4$$

Do the multiplications in 2x^{5}-3\times 9x^{2}.

$$\frac{2x^{5}-27x^{2}}{6}+7x-4$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 7x-4 times \frac{6}{6}.

$$\frac{2x^{5}-27x^{2}}{6}+\frac{6\left(7x-4\right)}{6}$$

Since \frac{2x^{5}-27x^{2}}{6} and \frac{6\left(7x-4\right)}{6} have the same denominator, add them by adding their numerators.

$$\frac{2x^{5}-27x^{2}+6\left(7x-4\right)}{6}$$

Do the multiplications in 2x^{5}-27x^{2}+6\left(7x-4\right).

$$\frac{2x^{5}-27x^{2}+42x-24}{6}$$

Factor

$$\frac{2x^{5}-27x^{2}+42x-24}{6}$$

Solution Steps

Factor out \frac{1}{6}. Polynomial 2x^{5}-27x^{2}+42x-24 is not factored since it does not have any rational roots.

$$\frac{2x^{5}-27x^{2}+42x-24}{6}$$