If x100-2 x99-k is divisible by x-1- then the value of k is-A- 1B- -3C- 3D- -2

The correct option is A 1Given (x+1) is a factor. According to factor theorem, nbsp; For any polynomial f(x), if x a is a factor then f(a) = 0. Substitut ...

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Standard X

Mathematics

Remainder Theorem

If x100+2 x99...

Question

If $x^{100} + 2 x^{99} + k$ is divisible by $(x + 1)$ , then the value of $k$ is:

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Solution

The correct option is A 1
Given $(x + 1)$ is a factor.

According to factor theorem,
For any polynomial f(x), if x - a is a factor then f(a) = 0.

Substituting $x = - 1$ in the given expression will give zero.
$f (- 1) = 0$
$(- 1)^{100} + 2 \times (- 1)^{99} + k = 0$
$((- 1)^{2})^{50} + 2 \times (- 1) \times ((- 1)^{2})^{49} + k = 0$
$1 - 2 + k = 0$
$k = 1$

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

The correct option is A 1Given (x+1) is a factor. According to factor theorem, For any polynomial f(x), if x - a is a factor then f(a) = 0. Substituting x=−1 in the given expression will give zero. f(−1)=0 (−1)100+2×(−1)99+k=0 ((−1)2)50+2×(−1)×((−1)2)49+k=0 1−2+k=0 k=1

If $x^{100} + 2 x^{99} + k$ is divisible by $(x + 1)$ , then the value of $k$ is: