# Math Help - Dividing a Polynomial

1. ## Dividing a Polynomial

Q. The number $6x^2 + 6x$(x is a natural number) is always divisible by
a. 6
b. 18
c 12
d 6 and 12 both

I tried to solve it using a rule :- $(a^n + b^n)$ is always divisible by (a+b), (a-b) if n is even. In this case n is even and odd respectively. What approach should i adopt ?

2. Originally Posted by vivek_master146
Q. The number $6x^2 + 6x$(x is a natural number) is always divisible by
a. 6
b. 18
c 12
d 6 and 12 both

I tried to solve it using a rule :- $(a^n + b^n)$ is always divisible by (a+b), (a-b) if n is even. In this case n is even and odd respectively. What approach should i adopt ?

$6x^2+6x=6(x)(x+1)$

x and (x+1) are a pair of consecutive even and odd numbers so the product is even.