Homework reminder:  Sheet on alg. fractions Qu. 6 h and i the Qu. 7 b, c, d.

See you Tues,

If you look at Example 8 on page 9, you’ll see how you can sometimes get a remainder when you finish the division. It’s a pretty simple extension of what you’ve done before. Significance of having a remainder? It means that the thing you’re dividing by (in that example (x-4) is not a factor of 2x^3 – 5x^2 -16x + 10.

Then if you look at Example 7, it’s simply showing an example of when you get a ‘zero’ bit part way through. If that happens, you just bring down the next bit of the polynomial. May be best if I go through that in person.

Factor Theorem:

The Factor Theorem is really simple. It just states that for any polynomial f(x), if f(p) = 0, then (x – p) is a factor of f(x).

Eg, show (x – 2) is a factor of  x^3 + x^2 – 4x – 4 

f(2) = 2^3  + 2^2 – (4 x 2) – 4 = 0, so (x – 2) is a factor.

You have to learn the basic proof of this, which is in Example 12 on page 12.

Do Ex 1D