Solve x^3+4x^2+4x-16

$$x ^ { 3 } + 4 x ^ { 2 } + 4 x - 16$$

Differentiate w.r.t. x

$$\left(x+2\right)\left(3x+2\right)$$

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}.

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

Subtract 1 from 3.

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

Multiply 2 times 4.

$$3x^{2}+8x^{2-1}+4x^{1-1}$$

Subtract 1 from 2.

$$3x^{2}+8x^{1}+4x^{1-1}$$

Subtract 1 from 1.

$$3x^{2}+8x^{1}+4x^{0}$$

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

$$3x^{2}+8x+4x^{0}$$

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

$$3x^{2}+8x+4\times 1$$

For any term t, t\times 1=t and 1t=t.

$$3x^{2}+8x+4$$

Evaluate

$$x^{3}+4x^{2}+4x-16$$