Question

If x¹⁴⁰+2x¹⁵¹ +k is divisible by x+1, then the value of k is
A. 1
B. -3
C. 2
D. -2

Answer 1

Answer:

k=1

Step-by-step explanation:

x+1=0

x=-1

substitute x=-1 in the equation

we have

1+2(-1)+k=0

1-2+k=0

-1+k=0

k=1

Answer 2

Given : x¹⁴⁰ + 2x¹⁵¹ + k is divisible by x + 1.

Solution :  

Let f (x) = x¹⁴⁰ + 2x¹⁵¹ + k

Since, x + 1 is a factor of f (x) then f (- 1) = 0

On Substituting x = - 1 in f (x),

(-1)¹⁴⁰ + 2(-1)¹⁵¹ + k = 0

1 - 2 + k = 0

k = 2 - 1

k = 1

Hence, the value of k is 1.

Among the given options option (A) 1 is correct.

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If x+1 is a factor if the polynomial 2x²+kx, then k =

A. -2

B. -3

C. 4

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(x+1) is a factor of xⁿ+1 only if

A. n is an odd integer

B. n is an even integer

C. n is a negative integer

D. n is a positive integer

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