Let us factorise the following polynomials:

x³ + 2x + 3

Given, f(x)= x³ + 2x + 3

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

Since, each term of f(x) is positive here; so for positive value of x we shall not get the value of f(x) as zero.

Hence, for the negative value of x, the value of f(x) can be zero.

f(−1)=(−1)³+2.(−1)+3=0

We observe that f(−1) = 0

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

x³ + 2x + 3 = x³ + x² – x² – x + 3x + 3

= x²(x+1)−x(x+1)+3(x+1)

= (x+1)(x²−x+3)