Solve p^2+12p

$$p ^ { 2 } + 12 p$$

Factor

$$p\left(p+12\right)$$

Solution Steps

Factor out p.

$$p\left(p+12\right)$$

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.

$$p^{2}+12p=0$$

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.

$$p=\frac{-12±\sqrt{12^{2}}}{2}$$

Take the square root of 12^{2}.

$$p=\frac{-12±12}{2}$$

Now solve the equation p=\frac{-12±12}{2} when ± is plus. Add -12 to 12.

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

Divide 0 by 2.

$$p=0$$

Now solve the equation p=\frac{-12±12}{2} when ± is minus. Subtract 12 from -12.

$$p=-\frac{24}{2}$$

Divide -24 by 2.

$$p=-12$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 0 for x_{1} and -12 for x_{2}.

$$p^{2}+12p=p\left(p-\left(-12\right)\right)$$

Simplify all the expressions of the form p-\left(-q\right) to p+q.

$$p^{2}+12p=p\left(p+12\right)$$

Evaluate

$$p\left(p+12\right)$$