Solve q^2-4q

$$q ^ { 2 } - 4 q$$

Factor

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

Solution Steps

Factor out q.

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

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.

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

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.

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

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

$$q=\frac{-\left(-4\right)±4}{2}$$

The opposite of -4 is 4.

$$q=\frac{4±4}{2}$$

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

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

Divide 8 by 2.

$$q=4$$

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

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

Divide 0 by 2.

$$q=0$$

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}.

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

Evaluate

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