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### Algebra Refresher

```
Date: 12/31/97 at 11:49:42
From: Aileene Cottrell
Subject: Need Help Immediately

Dear Dr. Math:

I am trying to get into an algebra class in college and am refreshing
my memory of what I learned in high school. Currently, I am trying to
figure out how to solve this equation: (x^3 + 3x^2 - 4x + 3) / (x+1).
If you can walk me through this and give me a formula that I can
always apply to get to the right answer, I'd really appreciate it.

Thanks,
Aileene
```

```
Date: 12/31/97 at 12:11:47
From: Doctor Rob
Subject: Re: Need Help Immediately

First of all, this is not an equation. There is no "=" sign. If you
mean to simplify this, it is already in simplest form. If you mean to
divide, giving quotient and remainder, here is how to proceed, using
long division:

-----------------------
x + 1 ) x^3 + 3*x^2 - 4*x + 3

Divide the leading term "x" of the divisor into the leading term "x^3"
of the dividend. The quotient is x^2. Put that above the 3*x^2 term of
the dividend, and above the line. Multiply that x^2 times the divisor,
putting the result below the dividend, and subtract. Bring down the
next term from the dividend into the current remainder. Your work
should look like this:

x^2
-----------------------
x + 1 ) x^3 + 3*x^2 - 4*x + 3
x^3 +   x^2
-------------
2*x^2 - 4*x

Now divide x into 2*x^2 to get the next term of the quotient. It is
2*x. Put it above the -4*x term of the dividend, and above the line.
Multiply that 2*x times the divisor, putting the result below the
current remainder, and subtract. Bring down the next term from the
dividend into the current remainder. Now you should have:

x^2 + 2*x
-----------------------
x + 1 ) x^3 + 3*x^2 - 4*x + 3
x^3 +   x^2
-------------
2*x^2 - 4*x
2*x^2 + 2*x
-------------
- 6*x + 3

Now divide x into -6*x to get the next term of the quotient. It is -6.
Put it above the +3 term of the dividend, and above the line. Multiply
that -6 times the divisor, putting the result below the current
remainder, and subtract.  Now you should have:

x^2 + 2*x - 6
-----------------------
x + 1 ) x^3 + 3*x^2 - 4*x + 3
x^3 +   x^2
-------------
2*x^2 - 4*x
2*x^2 + 2*x
-------------
- 6*x + 3
- 6*x - 6
-----------
9

You are done, because 9 involves no x's at all, and the divisor x + 1
has x to the first power, so you cannot divide x + 1 into 9.  The
quotient is the top line, x^2 + 2*x - 6, and the remainder is the
bottom line, 9.  This means (x^3 + 3*x^2 - 4*x + 3)/(x + 1) is x^2 +
2*x - 6 with remainder 9, or, in other words,

(x^3 + 3*x^2 - 4*x + 3)/(x + 1) = x^2 + 2*x - 6 + [9/(x+1)].

Notice that, reading down the columns, every term has the same
exponent of x.  This is the best way to arrange your work. Keeping

I hope that this was what you wanted. If not, write back to us again.

-Doctor Rob,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Basic Algebra
Middle School Algebra

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