Solve a^2-3a

$$a ^ { 2 } - 3 a$$

Factor

$$a\left(a-3\right)$$

Solution Steps

Factor out a.

$$a\left(a-3\right)$$

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.

$$a^{2}-3a=0$$

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.

$$a=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}}}{2}$$

Take the square root of \left(-3\right)^{2}.

$$a=\frac{-\left(-3\right)±3}{2}$$

The opposite of -3 is 3.

$$a=\frac{3±3}{2}$$

Now solve the equation a=\frac{3±3}{2} when ± is plus. Add 3 to 3.

$$a=\frac{6}{2}$$

Divide 6 by 2.

$$a=3$$

Now solve the equation a=\frac{3±3}{2} when ± is minus. Subtract 3 from 3.

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

Divide 0 by 2.

$$a=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 3 for x_{1} and 0 for x_{2}.

$$a^{2}-3a=\left(a-3\right)a$$

Evaluate

$$a\left(a-3\right)$$