Question

If $f\left(x\right)$ be divided by $(x–\alpha )$ and we obtain remainder $r\left(x\right)$ such that $r\left(x\right)\ne 0$, then which of the following is always correct?

• A. Degree of r(x) = Degree of $(x–\alpha )$
• B. Degree of r(x) > Degree of $(x–\alpha )$
• C. Degree of r(x) < Degree of $(x–\alpha )$
• D. Degree of $r\left(x\right)>1$

Answer 1

The correct option is C Degree of r(x) < Degree of $(x–\alpha )$

If f(x) is divided by $(x–\alpha )$, then the quotient is q(x) and the remainder is r(x) such that $r\left(x\right)\ne 0$.
$\therefore f\left(x\right)=(x–\alpha )\times q\left(x\right)+r\left(x\right)$
Also, Degree of remainder < Degree of divisor
Thus, degree of r(x) < degree of $(x–\alpha )$.
Hence, the correct answer is option (3)