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

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Solution

The correct option is D 7
$f (x) = 1 + x + x^{3} + x^{9} + x^{29} + x^{81} + x^{243}$
the remainder obtained by $f (x)$ when
divided by $x - 1$
is $f (1)$ by remainder theorem
$f (1) = 7$
So, remainder is 7

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