The remainder obtained when the polynomial $1 + x + x^{3} + x^{9} + x^{27} + x^{81} + x^{243}$ is divisible by $x - 1$ is

3

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5

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7

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11

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Solution

The correct option is C $7$
$p (x) = 1 + x + x^{3} + x^{9} + x^{27} + x^{81} + x^{243}$
Let $q (x)$ be the quotient when $P (x)$ divided by $(x - 1)$ .
Therefore,
$P (x) = (x - 1) \cdot q (x) + A$
$P (1) = (1 - 1) \cdot q (x) + A$
$7 = 0 + A$
$A = 7$
Hence the remainder is $7$ .

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The remainder obtained when the polynomial 1+x+x3+x9+x27+x81+x243 is divisible by x−1 is

The correct option is C 7p(x)=1+x+x3+x9+x27+x81+x243Let q(x) be the quotient when P(x) divided by (x−1).Therefore,P(x)=(x−1)⋅q(x)+AP(1)=(1−1)⋅q(x)+A7=0+AA=7Hence the remainder is 7.

The remainder obtained when the polynomial $1 + x + x^{3} + x^{9} + x^{27} + x^{81} + x^{243}$ is divisible by $x - 1$ is

The correct option is C $7$
$p (x) = 1 + x + x^{3} + x^{9} + x^{27} + x^{81} + x^{243}$
Let $q (x)$ be the quotient when $P (x)$ divided by $(x - 1)$ .
Therefore,
$P (x) = (x - 1) \cdot q (x) + A$
$P (1) = (1 - 1) \cdot q (x) + A$
$7 = 0 + A$
$A = 7$
Hence the remainder is $7$ .