Game Development Reference
In-Depth Information
moving in a negative direction. It shows a trend characterized by a moment of
maximum effectiveness preceded and followed by periods of increasing and
declining effectiveness.
Solving Equations
In previous chapters, when you have solved equations, you have put to work a
variety of tools that have allowed you to manipulate the expressions and terms
equations contain. These tools can be brought forward and extended as you solve
polynomial equations. Table 8.1 lists a few of the fundamental concepts you work
with as you solve polynomial equations. Subsequent sections of this chapter
elaborate on these concepts.
Addition and Subtraction Activities
When you add the terms that a polynomial contains, one of the first steps is to
group like terms. Like terms identify what you are adding. Here is an equation
with like terms:
2
x þ
3
x
In this instance, the terms of the equation constitute like terms because each term
consists of the variable
x
. Each of the like terms is associated with an integer
coefficient. To solve for
x
, you put the distributive property to work:
ð
2
þ
3
Þx ¼
5
x
Here is an extended example of the same type of operation:
6
x þ
7
x
4
x þ
8
x x
¼ð
6
x þ
7
xÞ
4
x þ
8
x x
¼ð
13
x
4
xÞþ
8
x x
¼ð
9
x þ
8
xÞx
¼ð
17
x xÞ
¼
16
x
For each step, you successively group like terms, and then carry out additions or
subtractions. In the end, you have combined all terms in the polynomial and are
left with the final term.
