Solve 2p^2-10p

$$2 p ^ { 2 } - 10 p$$

Factor

$$2p\left(p-5\right)$$

Solution Steps

Factor out 2.

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

Consider p^{2}-5p. Factor out p.

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

Rewrite the complete factored expression.

$$2p\left(p-5\right)$$

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.

$$2p^{2}-10p=0$$

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.

$$p=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}}}{2\times 2}$$

Take the square root of \left(-10\right)^{2}.

$$p=\frac{-\left(-10\right)±10}{2\times 2}$$

The opposite of -10 is 10.

$$p=\frac{10±10}{2\times 2}$$

Multiply 2 times 2.

$$p=\frac{10±10}{4}$$

Now solve the equation p=\frac{10±10}{4} when ± is plus. Add 10 to 10.

$$p=\frac{20}{4}$$

Divide 20 by 4.

$$p=5$$

Now solve the equation p=\frac{10±10}{4} when ± is minus. Subtract 10 from 10.

$$p=\frac{0}{4}$$

Divide 0 by 4.

$$p=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 5 for x_{1} and 0 for x_{2}.

$$2p^{2}-10p=2\left(p-5\right)p$$

Evaluate

$$2p\left(p-5\right)$$