Solve 3x^3+Qx^2+2x-4)=(x+2)

$$3 x ^ { 3 } + Q x ^ { 2 } + 2 x - 4 ) = ( x + 2 )$$

Differentiate w.r.t. x

$$9x^{2}+2Qx+2$$

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}.

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

Multiply 3 times 3.

$$9x^{3-1}+2Qx^{2-1}+2x^{1-1}$$

Subtract 1 from 3.

$$9x^{2}+2Qx^{2-1}+2x^{1-1}$$

Subtract 1 from 2.

$$9x^{2}+2Qx^{1}+2x^{1-1}$$

Subtract 1 from 1.

$$9x^{2}+2Qx^{1}+2x^{0}$$

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

$$9x^{2}+2Qx+2x^{0}$$

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

$$9x^{2}+2Qx+2\times 1$$

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

$$9x^{2}+2Qx+2$$

Evaluate

$$3x^{3}+Qx^{2}+2x-4$$