# Math 101 Review Sheet for Exam #2

## 5 Exponents and Polynomials

**5.1 Integer Exponents**

All of the rules you could possibly ever need to know are
summarized

on pages 289-290 in the big purple box. You will be asked to apply

these rules.

Problems 1-88 are practice problems leading up to the
problems

that we need to be able to solve. If you feel confident, dive into

any of 107-124. Do enough problems so you can solve 121 and 123

confidently , this looks like a good order of difficulty to me.

In addition, you might want to try the following. Simplify
until

all exponents are positive,

1.

Don’t worry about looking at scientific notation. This
wasn’t

covered in the homework or in class.

**5.2 Adding and Subtracting Polynomials **

This section is really practice leading up to the
important stuff:

multiplying and dividing polynomials . One common item you need

to be quick with is subtracting polynomials, because this shows up

so often when doing polynomial long division. You may want to try

problems 57, 58, 59, 60 or just wait until the long division section

to get practice doing this.

**5.3
**Skip this section.

**5.4 Multiplying Polynomials**

It’s important you know how to do simple multiplication,
such as

8-13 any.

It’s also important you know how to multiply polynomials
where

the FOIL method doesn’t work. (The big problem with this method

is it doesn’t generalize). 15-23 all look like excellent problems to take

a peek at.

83 and 84 also look like excellent problems.

**5.5 What’s next? Polynomial Division**

What can I say. Know how to do polynomial long division.
Know

how to deal with the remainder if it’ s not zero .

I think the most common error will be not subtracting all
terms

when it comes time to do the subtraction.

Problems 17-46 all look like excellent problems.

## 6 The Backwards Problem, Factoring Polynomials

After learning how to add, subtract, multiply and divide
polynomials,

now we do it in reverse order. Sections 6-1 through 6-4 seem a

bit jumbled up. I’ll point out what’s important from these sections,

then give you a lot of practice problems.

**6.1 Greatest Common Factors; Factoring by Grouping**

**6.2 Factoring Trinomials**

This section is really the heart of the chapter. The goal
is to get to

the point where you can factor trinomials which are polynomials of

the form ax^{2} + bx + c.

For our purposes, we will not ask you to determine if a
polynomial

is prime. Whatever problem shows up on the exam, you will be able

to factor it.

**6.3 Special Factoring**

We don’t want you to have to memorize a lot of formulas .
One

important factoring to keep in mind is using the formula

x^{2} − y^{2} = (x + y)(x − y).

For example, this can be used to factor

x^{2} − 169.

**6.4 A General Approach to Factoring**

This really seems like a better review section than
section inside the

chapter. Rather than work on these problems (there are many who

are prime, and some of them ask you to use special factorings that

we didn’t cover), I’ll give you practice problems here.

One thing to keep in mind is every time you’re asked to
factor

a polynomial, first look for a common factor that can be pulled

out. This will make your life so much easier! Remember this when

working on these problems.

2. Factor:

a) x^{2} + 4x − 21.

b) y^{2} + 3y − 10.

c) a^{2} + 3a − 130.

d) 4x^{2} + 32x + 28.

e) x^{3} − 4x.

f) j^{2} − j − 56.

g) 3x^{2} + 3x − 6.

h) z^{3} − 2z^{2} − 35z.

i) 2x^{2} − 18.

j) y^{2} + 3y − 130.

k) z^{3} − 4z^{2}

l) 5k^{2} − 20k + 225.

m) p^{2} − 24p + 144.

n) n^{2} + 14n + 49.

**6.5 Solving Equations by Factoring **

Do the homework problems. Below is an extremely brief
description

of what’s in this section.

This is where we solve our first non- linear equation ! In
order to

make any headway, we need to zero factor property , defined on page

360.

There are two tools to keep in mind when solving these
problems.

First, the problem may be handed to you on a silver platter, like

solve

**3.**

(x − 5)(x + 60) = 0.

More likely, the problem will require a bit of work,
namely factoring

a trinomial, and before that can be done you need to get all

your terms to one side . Similar to solve

**4.**

2x^{2} = 3 − x.

Sometimes when trying to solve something like

(3y + 2)(y − 3) = 7y − 1

one needs to do a bit of work. Now with this problem, some
idiot

decided to to a half job of factoring it. The left hand side is factored,

but in this case it doesn’t do us any good!

The tool to keep in mind, with a problem like this, is to
multiply

everything out first. Then after doing that, you can get all terms to

one side, and you’ve reduced it down to factoring a trinomial.

So, with that being said,

**5.** Find the solution set for

(3y + 2)(y − 3) = 7y − 1.

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