Solve 3(x)^(3)-5(x)^(2)-11x-3\div(x-3)

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Question

$$3 { x }^{ 3 } -5 { x }^{ 2 } -11x-3 \div (x-3)$$

Evaluate

$\frac{3x^{4}-14x^{3}+4x^{2}+33x-3}{x-3}$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply $3x^{3}-5x^{2}-11x$ times $\frac{x-3}{x-3}$.

$$\frac{\left(3x^{3}-5x^{2}-11x\right)\left(x-3\right)}{x-3}-\frac{3}{x-3}$$

Since $\frac{\left(3x^{3}-5x^{2}-11x\right)\left(x-3\right)}{x-3}$ and $\frac{3}{x-3}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(3x^{3}-5x^{2}-11x\right)\left(x-3\right)-3}{x-3}$$

Do the multiplications in $\left(3x^{3}-5x^{2}-11x\right)\left(x-3\right)-3$.

$$\frac{3x^{4}-9x^{3}-5x^{3}+15x^{2}-11x^{2}+33x-3}{x-3}$$

Combine like terms in $3x^{4}-9x^{3}-5x^{3}+15x^{2}-11x^{2}+33x-3$.

$$\frac{3x^{4}-14x^{3}+4x^{2}+33x-3}{x-3}$$

Show Solution

Differentiate w.r.t. x

$\frac{9x^{4}-64x^{3}+130x^{2}-24x-96}{\left(x-3\right)^{2}}$