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.

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

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

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

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

∴ q = 9 ( $x^{2} + 19 x - 5$ ) and r = 0

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Similar questions

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 -

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

x^{2} + x + 1

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If $({5 x}^{2} + 14 x + 2)^{2}$ – $({4 x}^{2} - 5 x + 7)^{2}$ is divided by $(x^{2} + x + 1)$ , then quotient q and remainder r are given by:

Find the remainder when $5 x^{2} + 14 x + 2$ is divided by $x - 4$ .

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