Solve x^3-4x^2-10*-12

$${ x }^{ 3 } -4 { x }^{ 2 } -10 \times -12$$

Evaluate

$$x^{3}-4x^{2}+120$$

Solution Steps

Multiply 10 and -12 to get -120.

$$x^{3}-4x^{2}-\left(-120\right)$$

The opposite of -120 is 120.

$$x^{3}-4x^{2}+120$$

Differentiate w.r.t. x

$$x\left(3x-8\right)$$

Steps Using Derivative Rule for Sum

Multiply 10 and -12 to get -120.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}-4x^{2}-\left(-120\right))$$

The opposite of -120 is 120.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}-4x^{2}+120)$$

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}.

$$3x^{3-1}+2\left(-4\right)x^{2-1}$$

Subtract 1 from 3.

$$3x^{2}+2\left(-4\right)x^{2-1}$$

Multiply 2 times -4.

$$3x^{2}-8x^{2-1}$$

Subtract 1 from 2.

$$3x^{2}-8x^{1}$$

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

$$3x^{2}-8x$$