Solve -x^3+30x^2-153x-100

$$- x ^ { 3 } + 30 x ^ { 2 } - 153 x - 100$$

Differentiate w.r.t. x

$$3\left(3-x\right)\left(x-17\right)$$

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}.

$$3\left(-1\right)x^{3-1}+2\times 30x^{2-1}-153x^{1-1}$$

Multiply 3 times -1.

$$-3x^{3-1}+2\times 30x^{2-1}-153x^{1-1}$$

Subtract 1 from 3.

$$-3x^{2}+2\times 30x^{2-1}-153x^{1-1}$$

Multiply 2 times 30.

$$-3x^{2}+60x^{2-1}-153x^{1-1}$$

Subtract 1 from 2.

$$-3x^{2}+60x^{1}-153x^{1-1}$$

Subtract 1 from 1.

$$-3x^{2}+60x^{1}-153x^{0}$$

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

$$-3x^{2}+60x-153x^{0}$$

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

$$-3x^{2}+60x-153$$

Evaluate

$$-x^{3}+30x^{2}-153x-100$$