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 ' $r$ ' respectively are _____.

(x^{2} + 19 x - 5), 0

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9 (x^{2} + 19 x - 5), 0

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(x^{2} + 19 x - 5), 1

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

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Solution

The correct option is B $9 (x^{2} + 19 x - 5), 0$
We have, $(5 x^{2} + 14 x + 2)^{2} - (4 x^{2} - 5 x + 7)$
$= (x^{2} + 19 x - 5) (9 x^{2} + 9 x + 9)$ ....Since $(a^{2} - b^{2} = (a + b) (a - b))$
$= 9 (x^{2} + 19 x - 5) (x^{2} + x + 1)$
Therefore, $q = 9 (x^{2} + 19 x - 5)$ and $r = 0$

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Similar questions

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

q

r

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

x^{2} + x + 1

Solve: $x^{2} + 19 x - 150$

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