Solve 6+4x^3-3xdiv2x-3

$$6 + 4 x ^ { 3 } - 3 x \div 2 x - 3$$

Evaluate

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

Short Solution Steps

Express \frac{3x}{2}x as a single fraction.

$$6+4x^{3}-\frac{3xx}{2}-3$$

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

$$6+4x^{3}-\frac{3x^{2}}{2}-3$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6+4x^{3} times \frac{2}{2}.

$$\frac{2\left(6+4x^{3}\right)}{2}-\frac{3x^{2}}{2}-3$$

Since \frac{2\left(6+4x^{3}\right)}{2} and \frac{3x^{2}}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(6+4x^{3}\right)-3x^{2}}{2}-3$$

Do the multiplications in 2\left(6+4x^{3}\right)-3x^{2}.

$$\frac{12+8x^{3}-3x^{2}}{2}-3$$

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

$$\frac{12+8x^{3}-3x^{2}}{2}-\frac{3\times 2}{2}$$

Since \frac{12+8x^{3}-3x^{2}}{2} and \frac{3\times 2}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{12+8x^{3}-3x^{2}-3\times 2}{2}$$

Do the multiplications in 12+8x^{3}-3x^{2}-3\times 2.

$$\frac{12+8x^{3}-3x^{2}-6}{2}$$

Combine like terms in 12+8x^{3}-3x^{2}-6.

$$\frac{6+8x^{3}-3x^{2}}{2}$$

Factor

$$\frac{8x^{3}-3x^{2}+6}{2}$$

Solution Steps

Factor out \frac{1}{2}. Polynomial 8x^{3}-3x^{2}+6 is not factored since it does not have any rational roots.

$$\frac{6+8x^{3}-3xx}{2}$$