Solve 6x^3+x^2-11x-10div2x+1

$$6 { x }^{ 3 } + { x }^{ 2 } -11x-10 \div 2x+1$$

Evaluate

$$6x^{3}+x^{2}-16x+1$$

Solution Steps

Divide 10 by 2 to get 5.

$$6x^{3}+x^{2}-11x-5x+1$$

Combine -11x and -5x to get -16x.

$$6x^{3}+x^{2}-16x+1$$

Differentiate w.r.t. x

$$2\left(9x-8\right)\left(x+1\right)$$

Steps Using Derivative Rule for Sum

Divide 10 by 2 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{3}+x^{2}-11x-5x+1)$$

Combine -11x and -5x to get -16x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{3}+x^{2}-16x+1)$$

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}.

$$3\times 6x^{3-1}+2x^{2-1}-16x^{1-1}$$

Multiply 3 times 6.

$$18x^{3-1}+2x^{2-1}-16x^{1-1}$$

Subtract 1 from 3.

$$18x^{2}+2x^{2-1}-16x^{1-1}$$

Subtract 1 from 2.

$$18x^{2}+2x^{1}-16x^{1-1}$$

Subtract 1 from 1.

$$18x^{2}+2x^{1}-16x^{0}$$

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

$$18x^{2}+2x-16x^{0}$$

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

$$18x^{2}+2x-16$$