# Thread: Qustion on the remainder theorem:

1. ## Qustion on the remainder theorem:

When P(z) is divided by (z^2) - 3z + z the remainder is 4z-7. Find the remainder when P(z) is divided by:

a) (z-1)

b) (z-2)

2. Originally Posted by karldiesen
When P(z) is divided by (z^2) - 3z + z the remainder is 4z-7. Find the remainder when P(z) is divided by:
a) (z-1)
b) (z-2)
Please review this posting. Is that really what the question says?

3. no, it was just a weird way of writing a quadratic equation!

4. Originally Posted by karldiesen
When P(z) is divided by (z^2) - 3z + z the remainder is 4z-7. Find the remainder when P(z) is divided by:
a) (z-1)
b) (z-2)
Originally Posted by Plato
Please review this posting. Is that really what the question says?
Originally Posted by karldiesen
no, it was just a weird way of writing a quadratic equation!
I am will to wager that is incorrect.
I bet that it is $\displaystyle z^2-3z\color{blue}+2$.
It is the only way to make sense of the question.

Theorem: If the polynomial $\displaystyle P(x)$ is divided by $\displaystyle x-a$ then the remainder is $\displaystyle P(a)$.

In this problem we have $\displaystyle P(z)=(z^2-3z+2)Q(z)+(4z-7)$.
Now use the theorem,

5. Originally Posted by Plato
I am will to wager that is incorrect.
I bet that it is $\displaystyle z^2-3z\color{blue}+2$.
It is the only way to make sense of the question.

Theorem: If the polynomial $\displaystyle P(x)$ is divided by $\displaystyle x-a$ then the remainder is $\displaystyle P(a)$.

In this problem we have $\displaystyle P(z)=(z^2-3z+2)Q(z)+(4z-7)$.
Now use the theorem,
You are absolutely correct, that is what I was trying to write. I just didn't know how to write the exponents!

But I am still stuck! I just can't see how I can get a solution...

6. What are $\displaystyle P(1)~\&~P(2)?$

7. They are equal to the remainder!

8. Originally Posted by karldiesen
They are equal to the remainder!
Theorem: If the polynomial $\displaystyle P(x)$ is divided by $\displaystyle x-a$ then the remainder is $\displaystyle P(a)$.
Theorem: If the polynomial $\displaystyle P(x)$ is divided by $\displaystyle x-a$ then the remainder is $\displaystyle P(a)$.