Solve 8x^3-36x^2+48x-27

$$8 x ^ { 3 } - 36 x ^ { 2 } + 48 x - 27$$

Differentiate w.r.t. x

$$24\left(x-2\right)\left(x-1\right)$$

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}.

$$3\times 8x^{3-1}+2\left(-36\right)x^{2-1}+48x^{1-1}$$

Multiply 3 times 8.

$$24x^{3-1}+2\left(-36\right)x^{2-1}+48x^{1-1}$$

Subtract 1 from 3.

$$24x^{2}+2\left(-36\right)x^{2-1}+48x^{1-1}$$

Multiply 2 times -36.

$$24x^{2}-72x^{2-1}+48x^{1-1}$$

Subtract 1 from 2.

$$24x^{2}-72x^{1}+48x^{1-1}$$

Subtract 1 from 1.

$$24x^{2}-72x^{1}+48x^{0}$$

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

$$24x^{2}-72x+48x^{0}$$

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

$$24x^{2}-72x+48\times 1$$

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

$$24x^{2}-72x+48$$

Evaluate

$$8x^{3}-36x^{2}+48x-27$$