Chapter 4.2, Problem 5AYU

5. $f\left(x\right)=q(x)g\left(x\right)+r(x)$, the function $r\left(x\right)$ is called the ______ .

(a) remainder       (b) dividend       (c) quotient       (d) divisor

To determine

To fill: The expression $f\left(x\right) = q\left(x\right) . g\left(x\right) + r\left(x\right)$

The function $r\left(x\right)$ is called the

Answer to Problem 5AYU

$f\left(x\right) = q\left(x\right) . g\left(x\right) + r\left(x\right)$

$r\left(x\right) = remainder$.

Explanation of Solution

Given:

$f\left(x\right) = q\left(x\right) . g\left(x\right) + r\left(x\right)$

By division algorithm.

$\text{Dividend = divisor}\text{ . quotient + remainder}$

$f\left(x\right) = Dividend$.

$q\left(x\right) = quotient$.

$g\left(x\right) = divisor$.

$r\left(x\right) = remainder$.