If x⁵¹ + 51 is divided by x + 1, the remainder is
a. 0
b. 1
c. 49
d. 50

Solution:

Consider p(x) = x⁵¹ + 51

If p(x) is divided by x + 1 the remainder we obtain is p(-1)

By substituting x = -1 we get

p(-1) = (-1)⁵¹ + 51

By further calculation

p(-1) = -1 + 51

p(-1) = 50

Therefore, the remainder is 50.

✦ Try This: If x³¹ + 31 is divided by x - 1, the remainder is

Consider p(x) = x³¹ + 31

If p(x) is divided by x - 1 the remainder we obtain is p(1)

By substituting x = 1 we get

p(1) = (1)³¹ + 31

By further calculation

p(1) = 1 + 31

p(1) = 32

Therefore, the remainder is 32.

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2

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NCERT Exemplar Class 9 Maths Exercise 2.1 Problem 11

If x⁵¹ + 51 is divided by x + 1, the remainder is a. 0, b. 1, c. 49, d. 50

Summary:

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