If the quotient of $x^{4} - 11 x^{3} + 44 x^{2} - 76 x + 48$ . When divided by $(x^{2} - 7 x + 12)$ is $A x^{2} + B x + C$ , then the descending order of A, B, C is :

A, B, C

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B, C, A

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A, C, B

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C, A, B

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Solution

The correct option is D C, A, B
On divinding $x^{4} - 11 x^{3} + 44 x^{2} - 76 x + 48$
by $x^{2} - 7 x + 12$ , we obtain the quotient $x^{2} - 4 x + 4$
So, $A x^{2} + B x + C = x^{2} - 4 x + 4$
$∴ A = 1, B = - 4, C = 4$
In descending order C, A, B.

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