Solve 10x^3-37x^2+10x+28)div(5x-6)

$$10 x ^ { 3 } - 37 x ^ { 2 } + 10 x + 28 ) \div ( 5 x - 6 )$$

Differentiate w.r.t. x

$$30x^{2}-74x+10$$

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}.

$$3\times 10x^{3-1}+2\left(-37\right)x^{2-1}+10x^{1-1}$$

Multiply 3 times 10.

$$30x^{3-1}+2\left(-37\right)x^{2-1}+10x^{1-1}$$

Subtract 1 from 3.

$$30x^{2}+2\left(-37\right)x^{2-1}+10x^{1-1}$$

Multiply 2 times -37.

$$30x^{2}-74x^{2-1}+10x^{1-1}$$

Subtract 1 from 2.

$$30x^{2}-74x^{1}+10x^{1-1}$$

Subtract 1 from 1.

$$30x^{2}-74x^{1}+10x^{0}$$

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

$$30x^{2}-74x+10x^{0}$$

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

$$30x^{2}-74x+10\times 1$$

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

$$30x^{2}-74x+10$$

Evaluate

$$10x^{3}-37x^{2}+10x+28$$