Math 154B Exam 2 Review

Your exam will be on THURSDAY, MARCH 19^th. It will cover Chapter 7 and have a value of 125 points.
You will have the entire time, lecture and lab, to take the exam. That’s from 11:00 until 1:15, 2 hours and
15 minutes. It will model the Chapter 7 Practice Test in your book on page 463, problems 3 – 25. You need
to be able to:

A. Factor polynomial expressions using the following guidelines:

1) IF APPROPRIATE, WRITE YOUR POLYNOMIAL IN STANDARD FORM.

2) IF A GREATEST COMMON FACTOR (GCF) EXISTS, FACTOR IT OUT OF EVERY
TERM IN THE POLYNOMIAL . IF YOUR LEADING COEFFICIENT IS NEGATIVE , YOU
SHOULD FACTOR OUT THE NEGATIVE WITH YOUR GCF. BE SURE TO INCLUDE
THIS FACTOR IN YOUR FINAL ANSWER.

3) IF THE POLYNOMIAL IS A BINOMIAL LOOK FOR THE DIFFERENCE OF SQUARES
PATTERN

A² – B² = (A + B)(A – B)

OR THE DIFFERENCE OF CUBES PATTERN

A³ – B³ = (A – B)(A² + AB + B²)

OR THE SUM OF CUBES PATTERN

A³ + B³ = (A + B)(A² – AB + B²)

4) IF THE POLYNOMIAL IS A TRINOMIAL:

A) LOOK FOR THE PERFECT SQUARE TRINOMIAL PATTERN.

A² + 2AB + B² = (A + B)² or A² – 2AB + B² = (A – B)²

B) OTHERWISE, FACTOR BY TRIAL AND ERROR.

5) IF THE POLYNOMIAL HAS FOUR TERMS, TRY FACTORING BY GROUPING .

6) IF AT THIS POINT YOU FIND A COMMON FACTOR IN ONE OF YOUR FACTORS, FACTOR
IT OUT.

7) CHECK BY MULTIPLYING .

B. Solve quadratic equations using the factoring method:
1) Put the equation into standard form.
2) Factor the polynomial side of the equation, if possible. (When the polynomial can’t be
factored, this method won 't work.)
3) Apply the Zero- Factor Property , setting each factor containing a variable equal to zero.
4) Solve the equations formed in step 3.
5) Check your solutions in the original equation.

C. Solve word problems that result in quadratic equations by
1) making a sketch if possible and defining your variable (s)
2) setting up the appropriate quadratic equation based on the information in the problem
3) solving the equation and finding all of the answers
4) writing a complete sentence conclusion.