Math 102 - Review Stuff You Should Know

1) The Distributive Property
• You can distribute something that’s multiplied by a set of parentheses whenever the
stuff inside the parentheses is added or subtracted. (Page 61)
• You CAN NOT distribute an exponent on a set of parentheses when the stuff inside is
added or subtracted. EVER.
• You can distribute an exponent on a set of parentheses to all of the pieces inside if
the things inside are multiplied or divided. (Page 259)

2) Solving Linear Equations
• You obviously need to be able to solve basic linear equations like the ones on page 100.
• I expect that you know, and CAN EXPLAIN, what it means to be a solution to an
equation. Also, keep in mind that there is a difference between A solution and THE
solution. A solution is simply a number that makes the equation a true statement when
you plug it in for the variable. The solution is ALL numbers that do this.
• Remember that it’s often a good idea to multiply out any parentheses and combine
any like terms at the beginning of solving. (But not always!)
example:(x + 3)(x − 2) = 0.
Multiplying out the parentheses here would be goofy – in fact, it would be the opposite
of what you want to do! The equation is already in a form that makes it easy to solve -
you just set each piece equal to zero and solve to get x = −3,2. (More on these later)
• Remember that if an equation contains fractions, it’s always a good idea to multiply
both sides by the common denominator as the very first step. This will get rid of all the
fractions (if you do it correctly).
• Unless you’re a jerk, you’ll want to check your answer to pretty much every equation
you solve by plugging it back in for the variable. (This is especially easy since you can
use a calculator if you get a weird answer, like 11/4)

3) Plugging Numbers Into Expressions
• This is not terribly difficult, but is terribly important. Make sure that you know
what it means to plug a number in for a variable. Also, keep in mind that sometimes
expressions have more than one letter, and so I can give you a number to plug in for each
of the variables.
• After you have plugged numbers into an expression, getting a final answer usually
requires doing some arithmetic. BE CAREFUL, especially if the problem includes negative
signs or fractions. I know you all can do arithmetic – if you screw up, it’s probably
because you just weren’t concentrating. Keep the order of operations in mind:
Parentheses come first, then exponents, then multiplication/division, and finally
addition/subtraction.

4) Basics of Graphing
• If you don’t know how to plot points, you’re screwed right from the start, so make
sure you’re comfortable with that. (Page 174)
• Remember that I absolutely will test you to see if you understand what the graph of
an equation really is. You need to understand that if you plug in 5 for x, and solve for y,
and you get 3, that means that the point (5, 3) is on the graph. Also, you need to
understand that if you know first that (5, 3) is on the graph, then I guarantee that if
you plug in 5 for x, you will get out 3 for y. This is what it means to understand what
graphs are.
• Finding points on a graph is easy if you understand the above - you just have to pick
any damn numbers and plug them in for one of the variables, and solve for the other.
This will give you pairs of numbers which you can plot and then connect the dots. Easy.
(Section 3.1)
• The easiest damn points you can find would come from plugging zero in for x, and
plugging zero in for y (separately, of course). These are what we call the intercepts.
The x-intercept is the point you get when you plug in zero for y, and the y-intercept is
the point you get when you plug in zero for x. (Page 178)

5) Factoring
• Like pretty much everything else in math, if you don’t have any idea what factoring
is, it’s probably going to be really hard to learn how to do it. So remember that
factoring is nothing other than taking something and writing it as a product. An example
would be 15 = 3 ⋅ 5. We have factored the number 15 here. That’s all that factoring is –
it just looks harder when you do it to expressions instead of numbers.
• The most basic thing you can do in factoring, and the first thing you should always
think about when you are asked to factor something, is to look and see if there is
something that is common to all of the terms which can be factored out, like in the first
factoring question on the pretest.
• The most common type of factoring we do is backwards FOIL. (If you don’t know
what FOIL is, see page 291.) This would be like the second and third factoring problems
on the pretest. For info and practice on this procedure, see sections 5.3 and 5.4.
• There are a handful of special formulas for factoring that we need from time to
time. The most important of these is the difference of squares formula – it comes up all
the time. Two others that we occasionally use are the sum and difference of cubes.
(See page 353.) Remember that if you need the sum or difference of cubes formulas, I
will supply them for you, but that may not be the case when you get to precalc.
• A fancy kind of factoring that we saw before is factoring by grouping. This works
sometimes on things that have four terms when there is nothing common that can be
factored out. See page 332.

6) Solving Equations That Are Not Linear
• First of all, any equation that contains any power of the variable other than one is
not linear, and the simple methods that work for linear equations just plain won’t work.
For any other equation, the only choice you have is to put everything on one side, zero on
the other, and factor. (See section 5.6)
• I want you to understand why this should work. Lookit an easy example:
(x + 3)(x − 2) = 0. What this equation is saying, if you think of it in words (which is
almost always helpful, by the way) is that the product of two numbers, one called x + 3,
and the other called x – 2, happens to be zero. Common sense tells me that if I multiply
together two numbers and get zero, one of those two numbers must be zero (duh). So
(x + 3)(x − 2) = 0 can be changed into either x + 3 = 0 or x − 2 = 0. Now we have two
linear equations that we know how to solve. That’s what solving non-linear equations is
all about.