x³ + 6x² + l lx + 6 is divisible by [2014 CDS-I]

Correct Answer is : All of the above

Correct Answer is : All of the above

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UPSC 2014 CDS I Math Paper

Question : 8 of 100

Marks: +1, -0

x^3 + 6x^2 + l lx + 6

Solution:

x^3+6x^2+11x+6

=x^3+x^2+5x^2+5x+6x+6

=x^2(x+1)+5x(x+1)+6(x+1)

=(x+1)(x^2+5x+6)

=(x+1)(x+2)(x+3)

So,

x^3+6x^2+11x+6

is divisible by

(x+1)(x+2)

and

(x+3)

Hit and Trial Method:

Option (a): Putting

x=-1

in the given expression, we have

(-1)^3+6(-1)^2+11(-1)+6=0

\Rightarrow (x+1)

is factor

Option (b): Putting

x=-2

in the given expression, we have

(-2)^3+6(-2)^2+11(-2)+6=0

\Rightarrow (x+2)

is factor. Similarly, wecan see option (c) is a factor.

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