Solve -3p^2+12p

$$- 3 p ^ { 2 } + 12 p$$

Factor

$$3p\left(4-p\right)$$

Solution Steps

Factor out 3.

$$3\left(-p^{2}+4p\right)$$

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

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

Rewrite the complete factored expression.

$$3p\left(-p+4\right)$$

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.

$$-3p^{2}+12p=0$$

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.

$$p=\frac{-12±\sqrt{12^{2}}}{2\left(-3\right)}$$

Take the square root of 12^{2}.

$$p=\frac{-12±12}{2\left(-3\right)}$$

Multiply 2 times -3.

$$p=\frac{-12±12}{-6}$$

Now solve the equation p=\frac{-12±12}{-6} when ± is plus. Add -12 to 12.

$$p=\frac{0}{-6}$$

Divide 0 by -6.

$$p=0$$

Now solve the equation p=\frac{-12±12}{-6} when ± is minus. Subtract 12 from -12.

$$p=-\frac{24}{-6}$$

Divide -24 by -6.

$$p=4$$

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 4 for x_{2}.

$$-3p^{2}+12p=-3p\left(p-4\right)$$

Evaluate

$$3p\left(4-p\right)$$