Question

Using factor theorem, factorize the polynomials: 

x³ + 6x² + 11x + 6

Answer 1

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).