Let f(x) = x3 + 6x2 + 11x + 6
Step 1: Find the factors of constant term
Here constant term = 6
Factors of 6 are ±1, ±2, ±3, ±6
Step 2: Find the factors of f(x)
Let x + 1 = 0
⇒ x = -1
Put the value of x in f(x)
f(-1) = (−1)3 + 6(−1)2 + 11(−1) + 6
= -1 + 6 -11 + 6
= 12 – 12
= 0
So, (x + 1) is the factor of f(x)
Let x + 2 = 0
⇒ x = -2
Put the value of x in f(x)
f(-2) = (−2)3 + 6(−2)2 + 11(−2) + 6
= - 8 + 24 – 22 + 6
= 0
So, (x + 2) is the factor of f(x)
Let x + 3 = 0
⇒ x = -3
Put the value of x in f(x)
f(-3) = (−3)3 + 6(−3)2 + 11(−3) + 6
= -27 + 54 – 33 + 6
= 0
So, (x + 3) is the factor of f(x)
Hence, f(x) = (x + 1)(x + 2)(x + 3).
