**PLEASE NOTE THAT YOU CANNOT USE A CALCULATOR ON THE
ACCUPLACER - ELEMENTARY ALGEBRA TEST! YOU MUST BE ABLE TO DO THE FOLLOWING
PROBLEMS WITHOUT A CALCULATOR!**

A quadratic equation in** x** is an equation that can
be written in the standard form

, where **a, b**, and **c **are real
numbers, but .

**A. Factoring Method - Some, but not all quadratic
equations can be solved by factoring.**

•Write the quadratic equation in standard form. That is,
using Properties of Equality, bring all

terms to one side of the equation so that the other side is equal to 0. Combine
like terms, if

possible.

•Factor relative to the integers.

•Use the Zero Product Principle to solve. It states that if a product is equal
to zero, then at least

one of the factors is equal to zero.

**Problem 1:**

Solve **15x^2 - 5x = 0** using the Factoring Method.
Find any real and imaginary solutions.

The quadratic equation is already in standard form so that we can factor as
follows:

By the Zero Product Principle we can the say

Therefore,

** Check:**

Please note that if we check these solutions in the
original equation, we find

the following:

Given **15x^2 - 5x = 0** and using **x = 0**, is**
15(0)^2 - 5(0)** equal to 0? Yes!

Therefore the solution is correct!

Given **15x^2 - 5x = 0** and using
, is equal to **0**? Yes,

because ! Therefore the solution is correct!

**Problem 2:**

Solve **x^2 + 5x = -6** using the Factoring Method.
Find any real and imaginary solutions.

Rewriting the equation in standard form yields **x^2 + 5x + 6 = 0**.

We notice that we have a trinomial, which we can factor as follows:

**(x + 3)(x + 2) = 0**

By the Zero Product Principle we can the say

x + 3 = 0 or x + 2 = 0

Therefore, **x = -3 or x = -2.**

Check:

Please note that if we check these solutions in the
original equation, we find

the following:

Given** x^2 + 5x = -6** and using **x = -3, is (-3)^2
+ 5(-3)** equal to **-6?** Yes!

Therefore the solution is correct!

Given **x^2 + 5x = -6** and using **x = -2,** is **
(-2)^2 + 5(-2)** equal to **-6**? Yes!

Therefore the solution is correct!

**Problem 3:**

Solve **x^2 - 4x + 4 = 0 **using the Factoring Method.
Find any real and imaginary

solutions.

We notice that we have a trinomial, which we can factor as follows:

**(x - 2)(x - 2) = 0**

By the Zero Product Principle we can the say

**x - 2 = 0 or x - 2 = 0**

Therefore, **x = 2** in both cases. Sometimes the **2**
is considered to be a double root.

**B. Square Root Method **- All quadratic equations can
be solved by this method which uses the

Square Root Property. However, we might want to avoid this method for some
quadratic equations

because it can get very cumbersome.

•Isolate the squared term on one side of the equation. Be
sure its coefficient is a positive 1 !!!!!!

•Apply the Square Root Property.

•If necessary, further isolate the variable.

**The Square Root Property**

If u is an algebraic expression containing a variable and
d is a constant, then

has exactly two solutions, namely

and or
simply