If $x^{2}$ - 6x + 11 is a factor of bi-quadratic equation $x^{4}$ + $x^{3}$ - 25 $x^{2}$ + 41x + 66 = 0. Find the product of other factor of bi-quadratic equation and x+1.

$x^{3} + 7 x^{2} + 5 x + 1$

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$x^{3} + x^{2} + x + 6$

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$x^{3} + 8 x^{2} + 13 x + 6$

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$x^{2} + 7 x + 6$

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Solution

The correct option is C
$x^{3} + 8 x^{2} + 13 x + 6$

$\begin{matrix} x^{2} + 7 x + 6 x^{2} - 6 x + 11 & x^{4} + x^{3} - 25 x^{2} + 41 x + 66_x^{4}_+ 6 x^{3}_- + 11 x^{2} 7 x^{3} - 36 x^{2}_{-} 7 x^{3}_{+} - 42 x^{2} + 77 x 6 x^{2} - 36 x + 66 6 x^{2} - 36 x + 66 0 \end{matrix} O t h e r f a c t o r i s x^{2} + 7 x + 6.$

Product of ( $x^{2}$ + 7x + 6) × (x + 1) = $x^{3}$ + 7 $x^{2}$ + 6x + $x^{2}$ + 7x + 6 = $x^{3}$ + 8 $x^{2}$ + 13x + 6

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If x2 - 6x + 11 is a factor of bi-quadratic equation x4 + x3- 25 x2 + 41x + 66 = 0. Find the product of other factor of bi-quadratic equation and x+1.

The correct option is C x3+8x2+13x+6 x2+7x+6x2−6x+11x4+x3−25x2+41x+66 _x4_+6x3_−+11x2 7x3−36x2 −7x3 +−42x2+77x 6x2−36x+66 6x2−36x+66 0 Otherfactorisx2+7x+6. Product of ( x2 + 7x + 6) × (x + 1) = x3 + 7 x2 + 6x + x2 + 7x + 6 = x3 + 8 x2 + 13x + 6

If $x^{2}$ - 6x + 11 is a factor of bi-quadratic equation $x^{4}$ + $x^{3}$ - 25 $x^{2}$ + 41x + 66 = 0. Find the product of other factor of bi-quadratic equation and x+1.