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Intermediate Algebra Exam 3 Study Guide

You are allowed a half page of notes (one side) and a scientific calculator.

For Exam 3 you will need to be able to:
1. Factor a polynomial by factoring out the GCF of all the terms. 7.1
2. Factor a polynomial by grouping. 7.2
3. Factor a trinomial with a leading coefficient that is one. 7.3
4. Factor a trinomial with a leading coefficient that is not one. 7.4
5. Factor a difference of squares. 7.5 You will not be asked to factor a difference or sum of cubes.
6. Factor a polynomial using a combination of factoring methods. 7.5

NOTE: For the factoring problems above, the only instructions I will give you on the exam will say: “Factor the
polynomial completely, or state that the polynomial is prime”. It will be up to you to figure out which factoring
‘tool’ or method to use. Read the handout I gave (General Strategy for Factoring Polys) or page 441 in the
textbook to see a strategy for factoring polynomials.

7. Solve a quadratic equation by factoring. 7.6
8. Solve an application problem by using a quadratic equation. There are several types: use the Pythagorean
Theorem to find an unknown side of a right triangle (page 456 #35); the equation is given and you need
to know how to use it to answer the question asked (page 457 #42); given the area of a rectangle find its
dimensions (page 456 #20) . 7.7
9. Find all numbers for which a rational expression is defined. 8.1
10. Simplify rational expressions. 8.1
11. Multiply two rational expressions. Simplify the result. 8.2
12. Divide two rational expressions. Simplify the result. 8.2
13. Add or subtract two rational expressions with the same denominator. Simplify the result, if possible. 8.3
14. Add or subtract two rational expressions with the different denominators. Simplify the result, if possible. 8.4
15. Solve a rational equation. Remember you have to check the proposed solution in the original equation to
eliminate any values that would make an expression undefined. The instructions I will give you will only
say: "Solve the equation". It is up to you to remember to check the answers. 8.6
16. Solve an application involving rational equations—motion problems (T= D/R) or work problems. I will not
give you these formulas, so if needed, write them on your index card. 8.7
17. Simplify square roots, including those that have radicands that are perfect squares, those that have radicands
that are not perfect squares, and those that have radicands with variables raised to various powers. 9.2
18. Simplify a quotient involving square roots. 9.2
19. Multiply two radical expressions by using the product rule and simplify if possible. 9.2
20. Multiply two radical expressions by using the distributive property or the FOIL method. If possible,
simplify any square roots that appear in the product. 9.3
21. Add or subtract radical expressions. You might need to simplify terms before they can be combined. 9.3
22. Given a radical expression, rationalize the denominator. You might need to first simply the expression, and
then rationalize the denominator. 9.4

• When factoring a polynomial, always look for a GCF first. If there is one, factor out the GCF before using any
other factoring method.
• Make sure to factor an expression completely, this means that you can’t factor any of the factors further
• You do not need an LCD when multiplying or dividing rational expressions. You only need the LCD
when you are adding or subtracting rational expressions.
• Find and keep the LCD when adding and subtracting rational expressions. Your final answer will look like a
rational expression, that is a fraction (unless the denominator cancels at the very end when you are simplifying the
final answer). Do not cancel any factors when adding or subtracting. The only time you may need to cancel factors
is at the end when you are trying to reduce the final answer.
• When subtracting rational expressions remember to distribute the minus sign to the entire numerator following the
subtraction sign.
• When solving an equation, find the LCD and then use it to cancel (get rid of) the denominators in an equation with
rational expressions. (This is when you want to cancel!) Your final answer should look like x = #. Of course, you
might have two answers or none!
• The last step when solving a rational equation is to check every solution (value) to see if it makes any term in the
original equation undefined (makes the denominator zero). If a value makes any term in the equation undefined,
this value is not a solution to the original rational equation.

Practice Problems

Chapter 7
Page 463 #7, 9, 10, 19, 21, 24

Also try:
Page 443 #78*
Page 450 #25, 53
Page 462 #65, 88, 102
Page 463 #132

*Answers to even problem:
#78 4(3n + 4)(n − 1)

Chapter 8
Page 534 #5, 9, 14, 20, 21, 24

Also try page 532 #2, 28, 48, 76

Chapter 9
Page 590 #6, 8, 10, 11, 16

Also try:
Page 588 #32