Anyways, we did the rational roots theorem and the synthetic divison.

The following questions for the rational roots theorem were:

Find each of the following and their domains: f

**O**g, g

**O**f, f

**O**f, g

**O**g.

f(x) = 2x+3, g(x) = 4x-1

f

**O**g(x) = f(g(x))

They're the same equation. What f

**O**g(x) means is that g is fed up inside of f which is the same as f(g(x)). Same goes for the other functions g

**O**f = g(f(x)), f

**O**f = f(f(x)), g

**O**g = g(g(x)).

Now lets try f

**O**g(x):

f(g(x)) = 2(4x-1)+3

= 8x-2+3

**= 8x+1**

Another function: f(x) = √x-1, g(x) = x^{2}

f

**O**g(x) = f(g(x))

= √x2-1

We cant simplify this any longer, so we leave it at that. Lets move on to...

Synthetic Division.

I hate dividing because it was too long. It eats up half of your paper when you do division but Mr. K showed us the easier way to divide.

For example:

The 7 on the left side is the root of x - 7. The 2 was brought down. Now 7 * 2 = 14, we put the 14 under 6. Then 14 + 6 = 20. We are now adding instead of subtracting compared to the long division. Subtraction can lead to different answers. We then multiply 7 * 20 = 140. We put the 140 on the next, under -40. Now we can add (-40) + 140 = 100. So we multiply 700 by 100 and we get 700, we add 700 to 1 and we get 701.

Now we have 2 20 100 701. We start on the very right side. We have 701 which is a remainder. So we put that as 701/x-7. Next up is 100. After the remainded we have the constant. So 100 is our constant. Next up is 20 and it becomes 20x and 2 becomes 2x^{2} . So we have 2x^{2} + 20x + 100 + 701/x-7.^{}

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