Question

According to Euclid's division Lemma for the two polynomials
$s\left(x\right)$ and $r\left(x\right)$ , we can write as $s\left(x\right)=p\left(x\right)\times q\left(x\right)+r\left(x\right)$. which of the following about $r\left(x\right)$ is/are true ?

• A. $r\left(x\right)$ can be zero
• B. Degree of $r\left(x\right)$ <0
• C. Degree of $r\left(x\right)$ >0
• D. $r\left(x\right)$ cannot be zero

Answer 1

Answer: (A), (B)

The correct options are
A $r\left(x\right)$ can be zero
B Degree of $r\left(x\right)$ <0

According to Euclid's division Lemma for the two polynomials
$s\left(x\right)$ and $r\left(x\right)$ , we can write as $s\left(x\right)=p\left(x\right)\times q\left(x\right)+r\left(x\right)$

Here, $r\left(x\right)$ can be zero or Degree of $r\left(x\right)$ <0