Solve 5p^2-20p

$$5 p ^ { 2 } - 20 p$$

Factor

$$5p\left(p-4\right)$$

Solution Steps

Factor out 5.

$$5\left(p^{2}-4p\right)$$

Consider p^{2}-4p. Factor out p.

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

Rewrite the complete factored expression.

$$5p\left(p-4\right)$$

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.

$$5p^{2}-20p=0$$

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.

$$p=\frac{-\left(-20\right)±\sqrt{\left(-20\right)^{2}}}{2\times 5}$$

Take the square root of \left(-20\right)^{2}.

$$p=\frac{-\left(-20\right)±20}{2\times 5}$$

The opposite of -20 is 20.

$$p=\frac{20±20}{2\times 5}$$

Multiply 2 times 5.

$$p=\frac{20±20}{10}$$

Now solve the equation p=\frac{20±20}{10} when ± is plus. Add 20 to 20.

$$p=\frac{40}{10}$$

Divide 40 by 10.

$$p=4$$

Now solve the equation p=\frac{20±20}{10} when ± is minus. Subtract 20 from 20.

$$p=\frac{0}{10}$$

Divide 0 by 10.

$$p=0$$

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}.

$$5p^{2}-20p=5\left(p-4\right)p$$

Evaluate

$$5p\left(p-4\right)$$