Question

If x + 2 is a factor of the expression (x + 1)^7 + (2x + k)^3, what is the value of k?​

Answer 1

Step-by-step explanation:

Because x + 2 is a factor of f(x)= (x+1)⁷ + (2x + k)³

Applying remainder theorem,

x+2 = 0

=> x = -2

f(-2) = (-2 + 1)⁷ + (2×-2 + k)³ = 0

=> -1 + (k-4)³ = 0

=> (k-4)³ = 1

=> k - 4 = 1

=> k = 5

Answer 2

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