Question

If on dividing a non-zero polynomial $p\left(x\right)$ by a polynomial $g\left(x\right)$, the remainder is zero, what is the relation between the degrees of $p\left(x\right)$ and $g\left(x\right)$?

• A. degree of $g\left(x\right)\ge$ degree of $p\left(x\right)$
• B. degree of $g\left(x\right)\le$ degree of $p\left(x\right)$
• C. degree of $g\left(x\right)=$ degree of $p\left(x\right)$
• D. Can't say

Answer 1

The correct option is B degree of $g\left(x\right)\le$ degree of $p\left(x\right)$

deg $p\left(x\right)=$ deg $g\left(x\right)+r\left(c\right)$

Then, deg $p\left(x\right)\ge$ deg $g\left(x\right)$