Solve {r}{8K^3-32K^2-88K}{+15-0}

$$\left. \begin{array} { r } { 8 K ^ { 3 } - 32 K ^ { 2 } - 88 K } \\ { + 15 - 0 } \end{array} \right.$$

Evaluate

$$8K^{3}-32K^{2}-88K+15$$

Solution Steps

Multiply -1 and 0 to get 0.

$$8K^{3}-32K^{2}-88K+15+0$$

Add 15 and 0 to get 15.

$$8K^{3}-32K^{2}-88K+15$$

Differentiate w.r.t. K

$$8\left(3K-11\right)\left(K+1\right)$$

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}.

$$3\times 8K^{3-1}+2\left(-32\right)K^{2-1}-88K^{1-1}$$

Multiply 3 times 8.

$$24K^{3-1}+2\left(-32\right)K^{2-1}-88K^{1-1}$$

Subtract 1 from 3.

$$24K^{2}+2\left(-32\right)K^{2-1}-88K^{1-1}$$

Multiply 2 times -32.

$$24K^{2}-64K^{2-1}-88K^{1-1}$$

Subtract 1 from 2.

$$24K^{2}-64K^{1}-88K^{1-1}$$

Subtract 1 from 1.

$$24K^{2}-64K^{1}-88K^{0}$$

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

$$24K^{2}-64K-88K^{0}$$

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

$$24K^{2}-64K-88$$