# Factor First, Then Solve the Equation - Set 1

### Explanation:

You will solve "quadratic equations" such as x² + 8x + 15 = 0. There are several steps. When you multiply and the answer is zero, one of the factors must have been zero. For instance, if x * y = 0, then either x = 0 or y = 0. If 3(x - 5) = 0 there are 2 factors, 3 and x - 5. Since 3 cannot be zero then x - 5 = 0, so x = 5. If x(x + 2) = 0 there are 2 factors, x and x + 2. Either x = 0 or x + 2 = 0, which means x = - 2. If (x + 3)(x - 4) = 0 then either x + 3 = 0 or x - 4 = 0, so x = - 3 or x = 4. The algebraic expression needs to be factored. Each factor is set equal to zero and the 1-step equations solved.

### Example(s):

Solve for x² - x - 6 = 0 Factor 1st: (x - 3)(x + 2) = 0 so x - 3 = 0 or x + 2 = 0 so x = 3 or x = - 2

Solve for x² + 16x + 28 = 0 1st: (x + 14)(x + 2) = 0 so x + 14 = 0 or x + 2 = 0 so x = - 14 or x = - 2

### Directions:

Equations for which the highest exponent for the variable is "2" are called "quadratic equations". These equations must be set equal to zero, then factored, then each factor is set equal to zero, then each 1-step equation is solved. Strive to be able to accomplish the problems with ease and then strive for speed. Good luck and enjoy the challenge!

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