Question

Factorise : x3 - 6x2 + 11x -6 using FACTOR THEOREM.

Answer 1

Solution is attached below

Answer 2

The factors are 1, 2, and 3

Step-by-step explanation:

According to Factor theorem, if (x - a) is a polynomial factor f(x), then f(a) = 0

Let $f(x) = x^{3}-6 x^{2}+11 x-6$

Let us check if (x - 1) is the factor of f(x),

Then,

$f(1) = 1^{3}-6\left(1^{2}\right)+11(1)-6=1-6+11-6=0$

Therefore (x-1) is a factor of f(x)

Let us check for the other factors

Hence,

$f(x)=(x-1)\left(x^{2}-5 x+6\right)$

$x^{2}-5 x+6=x^{2}-2 x-3 x+6$

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

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

$f(x) = (x - 1)(x - 2)(x - 3)$

Therefore, 1, 2, 3 are the factors of f(x)