Solve 3c^2+8c

$$3 c ^ { 2 } + 8 c$$

Factor

$$c\left(3c+8\right)$$

Solution Steps

Factor out c.

$$c\left(3c+8\right)$$

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.

$$3c^{2}+8c=0$$

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.

$$c=\frac{-8±\sqrt{8^{2}}}{2\times 3}$$

Take the square root of 8^{2}.

$$c=\frac{-8±8}{2\times 3}$$

Multiply 2 times 3.

$$c=\frac{-8±8}{6}$$

Now solve the equation c=\frac{-8±8}{6} when ± is plus. Add -8 to 8.

$$c=\frac{0}{6}$$

Divide 0 by 6.

$$c=0$$

Now solve the equation c=\frac{-8±8}{6} when ± is minus. Subtract 8 from -8.

$$c=-\frac{16}{6}$$

Reduce the fraction \frac{-16}{6} to lowest terms by extracting and canceling out 2.

$$c=-\frac{8}{3}$$

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 -\frac{8}{3} for x_{2}.

$$3c^{2}+8c=3c\left(c-\left(-\frac{8}{3}\right)\right)$$

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

$$3c^{2}+8c=3c\left(c+\frac{8}{3}\right)$$

Add \frac{8}{3} to c by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$3c^{2}+8c=3c\times \frac{3c+8}{3}$$

Cancel out 3, the greatest common factor in 3 and 3.

$$3c^{2}+8c=c\left(3c+8\right)$$

Evaluate

$$c\left(3c+8\right)$$