Questions | 5 |

Topics | Factoring Quadratics, Line Segment, Pythagorean Theorem, Quadratic Equations, Two Variables |

To factor a quadratic expression, apply the FOIL (**F**irst, **O**utside, **I**nside, **L**ast) method in reverse.

A line segment is a portion of a line with a measurable length. The **midpoint** of a line segment is the point exactly halfway between the endpoints. The midpoint **bisects** (cuts in half) the line segment.

The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the **hypotenuse** squared (c^{2}) is equal to the sum of the two perpendicular sides squared (a^{2} + b^{2}): c^{2 }= a^{2} + b^{2} or, solved for c, \(c = \sqrt{a + b}\)

When solving quadratic equations, if the equation is not set equal to zero, first manipulate the equation so that it is set equal to zero: ax^{2} + bx + c = 0. Then, factor the quadratic and, because it's set to zero, you know that one of the factors must equal zero for the equation to equal zero. Finding the value that will make each factor, i.e. (x + ?), equal to zero will give you the possible value(s) of x.

When solving an equation with two variables, replace the variables with the values given and then solve the now variable-free equation. (Remember order of operations, PEMDAS, **P**arentheses, **E**xponents, **M**ultiplication/**D**ivision, **A**ddition/**S**ubtraction.)