When $q (x) = 2 x^{3} - 5 x^{2} + 3 x + 7$ is divided by $x + 2$ , then the remainder is $R_{1}$ . The value of $R_{1}^{2}$ is

- 1225

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- 35

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1225

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35

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Solution

The correct option is C $1225$
$q (x) = 2 x^{3} - 5 x^{2} + 3 x + 7$
$x + 2 = 0 \Rightarrow x = - 2$
By remainder theorem,
$R_{1} = 2 (- 2)^{3} - 5 (- 2)^{2} + 3 (- 2) + 7$
$= - 16 - 20 - 6 + 7$
$R_{1} = - 35$
$R_{1}^{2} = (- 35)^{2} = 1225$
So, the correct answer is option (c).

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