Solve x^3-6x^2-15x+40

$${ x }^{ 3 } -6 { x }^{ 2 } -15x+40$$

Differentiate w.r.t. x

$$3\left(x-5\right)\left(x+1\right)$$

Steps Using Derivative Rule for Sum

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$3x^{3-1}+2\left(-6\right)x^{2-1}-15x^{1-1}$$

Subtract 1 from 3.

$$3x^{2}+2\left(-6\right)x^{2-1}-15x^{1-1}$$

Multiply 2 times -6.

$$3x^{2}-12x^{2-1}-15x^{1-1}$$

Subtract 1 from 2.

$$3x^{2}-12x^{1}-15x^{1-1}$$

Subtract 1 from 1.

$$3x^{2}-12x^{1}-15x^{0}$$

For any term t, t^{1}=t.

$$3x^{2}-12x-15x^{0}$$

For any term t except 0, t^{0}=1.

$$3x^{2}-12x-15$$

Evaluate

$$x^{3}-6x^{2}-15x+40$$