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)
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,