Question

Factorise : x^3-6x^2+11x-6 urgentt plzz !!!

Answer 1

Answer:

Step-by-step explanation:

Though it is cubic we have to find first root by hit and trial.

On doing this we get x=1 satisfy the equation

So( x-1)is the factor.

Thank you

Answer 2

f(x) = x³ - 6x² + 11x - 6

Let  us put f(1) in the polynomial

therefore

= (1)³ - 6(1)² + 11(1) - 6

= 1 - 6 + 11 - 6

= 0

On putting x = 1 we got remainder 0 , that means (x - 1) is a factor of f(x).

For other factors , we will divide f(x) by (x - 1)

∴ we get quotient g(x) = x² - 5x + 6

Factorising g(x)

= x² - 5x + 6

= x² - 3x - 2x + 6

= x( x - 3 ) - 2(x - 3)

= ( x - 3 ) ( x - 2 )

Hence, all the factors of f(x) = (x - 1)( x - 2 ) ( x - 3 )

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I hope you get it .