Final: Factor and Split

To solve a quadratic equation by factoring, factor the left side, then use the zero product rule. A product is zero only when one of its factors is zero, so set each factor equal to zero and solve. Then check both solutions in the original equation.

For example, to solve $x^{2}+5x+6 = 0$, look at the signs. The constant 6 is positive and the middle term is positive, so both numbers are positive. The pair 2 and 3 multiplies to 6 and adds to 5, so the equation is $\left(x+2\right)\left(x+3\right) = 0$. Setting each factor equal to zero gives $x = -2$ or $x = -3$. Both values make the original equation true.