JIPMAT 2024 (QA) - The factors of polynomial x^3-6 x^2+11 x-6 are : | PYQs + Solutions

JIPMAT 2024

Algebra

Quadratic Equations

Medium

The factors of polynomial $x^{3}-6 x^{2}+11 x-6$ are :

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

(x-1)(x+2)(x+3)

(x-1)(x-2)(x-3)

(x-1)(x-2)(x+3)

Correct Option: 3

Factors mean that each of these factors divide the polynomial perfectly. So, if we looked at Option 1, then:

\newline

x+1=x+2=x+3=0,

which would mean

x=-1,-2

-3

. These values, when put in the polynomial, should be equating 0. So, go by the options doing this. Look at Option 3.

Then,

x=1,2,3.

Putting

x=1

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

Putting

x=2

(2)^3-6(2)^2+11(2)-6=8-24+22-6=0

Putting

x=3

(3)^3-6(3)^2+11(3)-6=27-54+33-6=0

Hence, Option 3 is the answer.

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