Question

Find the remainder for the given division. (z^2+3z+1)/(z-2)

Answer 1

Step-by-step explanation

Given the expression

`(z^(2)+3z+1)/(z-2)`

We are asked to find the remainder. We can use the remainder theorem. This can be seen below.

According to this theorem, if we divide a polynomial P(x) by a factor ( x – a); that isn't essentially an element of the polynomial; you will find a smaller polynomial along with a remainder.

All we need to do is to substitute the value of (a) in the numerator to get the remainder. a is represented in the denominator.

Therefore, we will have;

`\begin{gathered} \text{ Remainder =}2^2+3(2)+1 \\ =4+6+1 \\ =10+1 \\ =11 \end{gathered}`