Foundation
Mathematics Foundation
Factor theorem
Question
If (x100 + 2x99 + k) is divisible by (x + 1) then the value of k is
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Solution
When a polynomial P(x) is divisible by (x – a), then by the Factor Theorem, P(a) = 0. Here, the divisor is (x + 1), which is equivalent to (x – (– 1)). Therefore, we substitute x = – 1 into the polynomial and set it equal to zero to solve for k.
So, we compute P(– 1): (− 1)100 + 2 × (− 1)99 + k = 0
This simplifies to: 1 + 2 × (– 1) + k = 0 → 1 – 2 + k = 0 → – 1 + k = 0
Therefore, k = 1.
Final Answer: 1