Question

If x^51+51 is divided by x+1, then the remainder is

(i) 0

(ii) 1

(iii) 49

(iv) 50​

Answer 1

Answer :-

• Remainder = 50 [option iv]

To Find :-

• $\tt \: The \: remainder \: if \: {x}^{51} + 51\: is \: divided \: by \: x + 1$

Step By Step Explanation :-

In this question we need to find the remainder.

So let's do it !!

Using Remainder theorem ⤵

$\tt \: p(x) = {x}^{51} + 51 \: and \: g(x) = x + 1 \\ \\ \tt \: g(x) = 0 \implies \: x + 1 = 0 \implies \: x = - 1$

By substituting the value of x ⤵

$\implies\sf {x}^{51} + 51 \\ \\\implies\sf { (- 1)}^{51} + 51 \\ \\\implies\sf - 1 + 51 \\ \\\implies\sf 50$

Therefore remainder of the given polynomial is => 50

More to Know :-

• Polynomial :- An algebraic expressions in which the variable involved having non negative integral power is known as polynomial.

• Variables :- A symbol which may be assigned different numerical values is known as a variable.

• Constants :- A symbol having a fixed numerical value is known as constant.

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