Let us factorise the following polynomials:

x³ – 3x +2

Given, f(x)= x³ – 3x +2

In f(x) putting x=±1, ±2, ±3, we see for which value of x, f(x)=0

f(1)=(1)³−3.(1)+2=0

We observe that f(1) = 0

From factor theorem, we can say, (x−1) is a factor of f(x)

x³ – 3x +2 = x³ – x² + x² − x − 2x +2

= x²(x−1)+x(x−1)−2(x−1)

= (x−1)(x²+x−2)

= (x−1)(x²+2x−x−2)

= (x−1)( x(x+2) – (x+2) )

= (x−1)(x−1)(x+2)

= (x−1)²(x+2)