####

#### Now let's investigate the product of f(x) and g(x)
when n = 0; therefore:

#### f(x) = -3

#### g(x) = 5

#### h(x) = -3 * 5 therefore h(x)
= -15

####

#### Again we get a straight line...will this continue?

####

#### What happens when we make n=6

#### f(x) = 6x - 3

#### g(x) = 6x + 5

#### h(x) = (6x - 3) (6x + 5)

####

#### Here it looks like the product
of two linear functions equals a quadratic function...will this
be the trend?

####

#### Let's look once more with n=20

#### f(x) = 20x - 3

#### g(x) = 20x + 5

#### h(x) = (20x - 3) (20x + 5)

####

#### Yes, another quadratic function...let's
break it down to see if this will always happen.

#### Suppose:

#### f(x) = ax + b

#### g(x) = cx + d

#### where a,b,c and d are real
numbers

#### Letting h(x) = f(x) * g(x);
h(x) = (ax + b) (cx + d)

#### Using the FOIL

#### h(x) = (ax)(cx) + (ax)d + (cx)b
+ bd

#### where h(x) = y

#### Since addition of real numbers
yield a real number we can say

#### p = ac

#### q = (ad + bc)

#### r = bd

#### such that p,q, and r are real
numbers

#### Therefore,

#### the general form of the quadratic
equation

####