Solve x^3-5x^2+3x+14

$$x ^ { 3 } - 5 x ^ { 2 } + 3 x + 14$$

Differentiate w.r.t. x

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

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}.

$$3x^{3-1}+2\left(-5\right)x^{2-1}+3x^{1-1}$$

Subtract 1 from 3.

$$3x^{2}+2\left(-5\right)x^{2-1}+3x^{1-1}$$

Multiply 2 times -5.

$$3x^{2}-10x^{2-1}+3x^{1-1}$$

Subtract 1 from 2.

$$3x^{2}-10x^{1}+3x^{1-1}$$

Subtract 1 from 1.

$$3x^{2}-10x^{1}+3x^{0}$$

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

$$3x^{2}-10x+3x^{0}$$

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

$$3x^{2}-10x+3\times 1$$

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

$$3x^{2}-10x+3$$

Evaluate

$$x^{3}-5x^{2}+3x+14$$