Solve P(c)=-12c^2+120c

$$P ( c ) = - 12 c ^ { 2 } + 120 c$$

Factor

$$12c\left(10-c\right)$$

Solution Steps

Factor out 12.

$$12\left(-c^{2}+10c\right)$$

Consider -c^{2}+10c. Factor out c.

$$c\left(-c+10\right)$$

Rewrite the complete factored expression.

$$12c\left(-c+10\right)$$

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.

$$-12c^{2}+120c=0$$

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.

$$c=\frac{-120±\sqrt{120^{2}}}{2\left(-12\right)}$$

Take the square root of 120^{2}.

$$c=\frac{-120±120}{2\left(-12\right)}$$

Multiply 2 times -12.

$$c=\frac{-120±120}{-24}$$

Now solve the equation c=\frac{-120±120}{-24} when ± is plus. Add -120 to 120.

$$c=\frac{0}{-24}$$

Divide 0 by -24.

$$c=0$$

Now solve the equation c=\frac{-120±120}{-24} when ± is minus. Subtract 120 from -120.

$$c=-\frac{240}{-24}$$

Divide -240 by -24.

$$c=10$$

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 10 for x_{2}.

$$-12c^{2}+120c=-12c\left(c-10\right)$$

Evaluate

$$12c\left(10-c\right)$$