Solve f(x)=-4x^3/3+5x^2-4x-1

$$f ( x ) = - \frac { 4 x ^ { 3 } } { 3 } + 5 x ^ { 2 } - 4 x - 1$$

Evaluate

$$-\frac{4x^{3}}{3}+5x^{2}-4x-1$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 5x^{2}-4x-1 times \frac{3}{3}.

$$-\frac{4x^{3}}{3}+\frac{3\left(5x^{2}-4x-1\right)}{3}$$

Since -\frac{4x^{3}}{3} and \frac{3\left(5x^{2}-4x-1\right)}{3} have the same denominator, add them by adding their numerators.

$$\frac{-4x^{3}+3\left(5x^{2}-4x-1\right)}{3}$$

Do the multiplications in -4x^{3}+3\left(5x^{2}-4x-1\right).

$$\frac{-4x^{3}+15x^{2}-12x-3}{3}$$

Factor

$$\frac{-4x^{3}+15x^{2}-12x-3}{3}$$

Solution Steps

Factor out \frac{1}{3}. Polynomial -4x^{3}+15x^{2}-12x-3 is not factored since it does not have any rational roots.

$$\frac{-4x^{3}+15x^{2}-12x-3}{3}$$