Question

If (x¹⁰⁰ + 2x⁹⁹ + k) is divided by (x + 1), then the value of k is

Answer 1

Answer:

k = 1

Step-by-step explanation:

As (x¹⁰⁰ + 2x⁹⁹ + k) is divided by (x + 1), x + 1 is a factor of (x¹⁰⁰ + 2x⁹⁹ + k).

We know that if x + a is factor of P(x) then, P(-a) = 0

So, here P(x) = (x¹⁰⁰ + 2x⁹⁹ + k) and a = -1

So, substituting, we get

P(-1) = [(-1)¹⁰⁰ + 2(-1)⁹⁹ + k] = 0

=> 1  + 2(-1) + k = 0

=> 1 - 2 + k = 0

=> -1 + k = 0

=> k - 1 = 0

$\therefore \underline {\boxed{k = 1}}$

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Answer 2

Answer:

As (x¹⁰⁰ + 2x⁹⁹ + k) is divided by (x + 1), x + 1 is a factor of (x¹⁰⁰ + 2x⁹⁹ + k).

We know that if x + a is factor of P(x) then, P(-a) = 0

So, here P(x) = (x¹⁰⁰ + 2x⁹⁹ + k) and a = -1

So, substituting, we get

P(-1) = [(-1)¹⁰⁰ + 2(-1)⁹⁹ + k] = 0

=> 1 + 2(-1) + k = 0

=> 1 - 2 + k = 0

=> -1 + k = 0

=> k - 1 = 0

➡ K=1

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