If $({5 x}^{2} + 14 x + 2)^{2}$ – $({4 x}^{2} + 14 x + 2)^{2}$ is divided by $(x^{2} + x + 1)$ , then quotient q and remainder r are given by -

q = (+19x-5), r = 1

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q = 9 (+19x-5), r = 0

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q = (+19x-5), r = 0

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q = 9 (+19x-5), r = 1

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Solution

The correct option is B
q = 9 (+19x-5), r = 0

Using $A^{2}$ - $B^{2}$ = (A + B) (A - B), we get:

Given Exp.

= ( ${5 x}^{2}$ +14x+2+ ${4 x}^{2}$ -5x+7) ( ${5 x}^{2}$ +14x+2- ${4 x}^{2}$ +5x-7)

= ( ${9 x}^{2}$ +9x+9) ( $x^{2}$ +19x-5)

= 9( $x^{2}$ +19x-5) ( $x^{2}$ +x+1)

= 9 ( $x^{2}$ +19x-5);

∴ q = 9 ( $x^{2}$ +19x-5) and r = 0

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