# ITM 107 Lecture Notes - Lecture 9: Quadratic Formula, Xterm, Social Security Trust Fund

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28 Nov 2018

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KATIE CHOI

11/5/18

LECTURE 7 QUADRATIC AND OTHER SPECIAL FUNCTIONS

Factoring Methods

• A quadratic equation in one variable is an equation that can be written in the general

form

• where a, b, and c represent constants. For example, the equations

are quadratic equations.

• When we solve quadratic equations, we will be interested only in real number solutions

and will consider two methods of solution: factoring and the quadratic formula.

• Solution by factoring is based on the following property of the real numbers.

• Zero Product Property

• Hence, to solve by factoring, we must first write the equation with zero on one side.

Example – Solving by Factoring

• Solve:

a)

b)

• Solution:

a) Note that the left side of the equation is factored, but the right member is

not 0. Therefore, we must multiply the factors before we can rewrite the

equation in general form.

b) The LCD of all fractions is x (3x + 6). Multiplying both sides of the equation by

this LCD gives a quadratic equation that is equivalent to the original equation

for x ≠ 0 and x ≠ –2. (The original equation is undefined for these values.)