MCQ
If $x^{51} + 51$ is divided by $x + 1, $the remainder is:
- A$0$
- B$1$
- C$49$
- ✓$50$
✓
Answer
Correct option: D.
$50$
When the polynomial $p(x)$ is divided by $q(x) \ i. e.\ (\text{x}\pm\alpha)$ then $\text{p}(\mp\alpha)$ is the remainder.
If $\text{x}\pm\alpha$ is the factor of polynomial, then remainder is $'0\ '.$
So,
If $x^{51} + 51$ is divided $x + 1.$
Remainder $= (-1)^{51} + 51 $
$= -1 + 51 $
$= 50.$
If $\text{x}\pm\alpha$ is the factor of polynomial, then remainder is $'0\ '.$
So,
If $x^{51} + 51$ is divided $x + 1.$
Remainder $= (-1)^{51} + 51 $
$= -1 + 51 $
$= 50.$
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