\( x^{3}\)+\(6x^{2} \)+\( 11x\)+\( 6\) is divisibke by


A) (\( x\)+\( 1\))only

B) (\( x\)+\( 2\))only

C) (\( x\)+\( 3\))only

D) All the above

Correct Answer:
D) All the above

Description for Correct answer:
From option (a)

x + 1 = 0 = > x = -1

For x = -1, \( \Large x^{3} + 6x^{2} + 11x + 6 \)

\( \Large = (-1)^{3} + 6(-1)^{2} + 11(-1) + 6 \)

= -1 + 6 - 11 + 6 = 0

Hence \( \Large x^{3} + 6x^{2} + 11x + 6 \) is divisible by x + 1.

From option (b)

x + 2 = 0 => x = -2

For x = -2

\( \Large = x^{3} + 6x^{2} + 11x + 6 \)

\( \Large = (-2)^{3} + 6(-2)^{2} + 11(-2) + 6 \)

= -8 + 24 - 22 + 6

= 30 - 30 = 0

Hence \( \Large x^{3} + 6x^{2} + 11x + 6 \) is also divisible by x + 2.

From option c

x + 3 = 0 = > x = -3

For x = -3,

\( \Large x^{3} + 6x^{2} + 11x +b \)

\( \Large = (-3)^{3} + 6(-3)^{2} + 11(-3) + 6 \)

= -27 + 54 - 33 + 6

= 60 - 60 = 0

Hence \( \Large x^{3} + 6x^{2} + 11x + 6 \) is also divisible by x + 3 = 0

Hence \( \Large x^{3} + 6x^{2} + 11x + 6 \) is also divisible by

(x + 1), (x + 2) and (x + 3)

option (d) is correct.

Part of solved CDS Maths(2) questions and answers : Exams >> CDSE >> CDS Maths(2)








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