The sum of all the coefficient of the polynomial $(x - 2)^{6} (x - 4)^{2} + (x + 1)^{3} + (x - 2)^{3} + (x + 1)^{2} (x - 4)^{3}$ is

- 92

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- 107

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- 152

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- 83

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Solution

The correct option is A $- 92$
${(x - 2)}^{6} {(x - 4)}^{2} + {(x + 1)}^{3} + {(x - 2)}^{3} + {(x + 1)}^{2} {(x - 4)}^{3}$
$t o f i n d t h e sum of coefficient of the polynomial put x=1$
${(1 - 2)}^{6} {(1 - 4)}^{2} + {(1 + 1)}^{3} + {(1 - 2)}^{3} + {(1 + 1)}^{2} {(1 - 4)}^{3}$
$= {(- 1)}^{6} {(- 3)}^{2} + {(2)}^{3} + {(- 1)}^{3} + {(2)}^{2} {(- 3)}^{3}$
$= 9 + 8 - 1 - 108$
$= - 92$

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