Find `k` if x⁵¹ +2x⁶⁰ +3x + k is divisible by x+1
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The answer is 2
Step-by-step explanation:
Given x⁵¹ + 2x⁶⁰ + 3x + k is divisible by x +1
That means x = -1
Substitute x = -1 in the expression
We know that (-1 ) ^ even = 1
( -1 ) ^ odd = - 1
(-1)⁵¹ + 2 (-1)⁶⁰ + 3 (-1) + k = 0
The expression is equal to zero as it is given that x +1 is a factor.
-1 +2 (1) -3 + k = 0
-1 +2 -3 +k = 0
-2 + k = 0
k = 2
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