If 2 divides x2+6x+9 then x + 3 would be a/an_____for any value of x, provided x2+6x+9 is a positive integer.
A
None of the above
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B
Odd Number
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C
Even Number
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D
Prime Number
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Solution
The correct option is C Even Number 2 divides x2+6x+9=(x+3)2 ⇒2 divides x+3 ( ∵ For any prime number p and a positive integer b, if p divides b2, then p divides b ) ⇒x+3 is even (∵ Numbers divisible by 2 are even)