Question

If on division of a polynomial p (x) by a polynomial g (x), the quotient is zero, what is the relation between the degrees of p (x) and g (x) ?

• A. deg p (x) < deg g (x)
• B. deg p (x) > deg g (x)
• C. Cannot be determined
• D. Can't say

Answer 1

The correct option is A deg p (x) < deg g (x)

By, Division Algorithm, we have
$p\left(x\right)=g\left(x\right)q\left(x\right)+r\left(x\right)$
If, on division of $p\left(x\right)$ by $g\left(x\right)$ the quotient is $0$, then the deg$p\left(x\right)<$deg$g\left(x\right)$
Ex: $p\left(x\right)=x+1$ and $g\left(x\right)=x^2-1$
Here, the quotient is $0$ and the deg$p\left(x\right)<$deg$g\left(x\right)$ ie $1<2$