Solve x^3-2x^2+x+16

$$x ^ { 3 } - 2 x ^ { 2 } + x + 16$$

Differentiate w.r.t. x

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

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}.

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

Subtract 1 from 3.

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

Multiply 2 times -2.

$$3x^{2}-4x^{2-1}+x^{1-1}$$

Subtract 1 from 2.

$$3x^{2}-4x^{1}+x^{1-1}$$

Subtract 1 from 1.

$$3x^{2}-4x^{1}+x^{0}$$

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

$$3x^{2}-4x+x^{0}$$

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

$$3x^{2}-4x+1$$

Evaluate

$$x^{3}-2x^{2}+x+16$$