Solve z^2-4z

$${ z }^{ 2 } -4z$$

Factor

$$z\left(z-4\right)$$

Solution Steps

Factor out z.

$$z\left(z-4\right)$$

Steps Using the Quadratic Formula

Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.

$$z^{2}-4z=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$z=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}}}{2}$$

Take the square root of \left(-4\right)^{2}.

$$z=\frac{-\left(-4\right)±4}{2}$$

The opposite of -4 is 4.

$$z=\frac{4±4}{2}$$

Now solve the equation z=\frac{4±4}{2} when ± is plus. Add 4 to 4.

$$z=\frac{8}{2}$$

Divide 8 by 2.

$$z=4$$

Now solve the equation z=\frac{4±4}{2} when ± is minus. Subtract 4 from 4.

$$z=\frac{0}{2}$$

Divide 0 by 2.

$$z=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 4 for x_{1} and 0 for x_{2}.

$$z^{2}-4z=\left(z-4\right)z$$

Evaluate

$$z\left(z-4\right)$$