Question

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

• A. q = (+19x-5), r = 1
• B. q = 9 (+19x-5), r = 0
• C. q = (+19x-5), r = 0
• D. q = 9 (+19x-5), r = 1

Answer 1

The correct option is B

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

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

Given expression,

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

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

= $9\times (x^2$+19x-5) ($x^2$+x+1)

=$9\times (x^2$+19x-5)

$\therefore$ $q=9(x^2$+19x-5) and r = 0