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### Sign Diagrams

```Date: 05/20/2002 at 03:43:17
From: Jessie
Subject: Sign Diagrams (without graphing)

There is a diagram in my text book that looks something like this:

x2 - 1/2x

|                |
+     |       _        |   +
__________________________________
|                |
-1/2               |

I have no idea what it's telling me.  Can you help me make sense of
it?
```

```
Date: 05/20/2002 at 12:24:14
From: Doctor Peterson
Subject: Re: Sign Diagrams (without graphing)

Hi, Jessie.

When you have a polynomial factored, you can find the sign of the
product by considering the sign of each factor separately. So let's
first factor our expression as

x^2 - 1/2 x = x(x - 1/2)

The first factor, x, will of course be positive when x > 0 and
negative when x < 0:

--------------0+++++++++++++  x
<-------------+------------>
0

The second factor, x - 1/2, will be positive when x > 1/2:

-------------------0++++++++  x - 1/2
<-------------+----+------->
0   1/2

Each factor has divided the number line into two parts, in different
ways. If we put these together, we make a total of three regions of
the number line, and can see what the product of the signs will be in
each region:

--------------0+++++++++++++  x
-------------------0++++++++  x - 1/2
++++++++++++++0----0++++++++  x(x - 1/2)
<-------------+----+------->
0   1/2

Whenever both factors are positive or both are negative, the product
will be positive; when one is positive and the other negative, the
product will be negative. That gives us a simple way to find the sign
of the expression everywhere.

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Polynomials

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