x# is defined for every positive even integer x as the product of all even integers from 2 to x. What is the smallest possible prime factor of (x#+7)?  Choose the correct choice.
A) 2 B) 3 C) 5 D) 7 E) 11
Since smallest possible prime factor is required.   Let x = 2 then --&gt; 2# = 2   x#+7 --  2= 
<gadget id="calculator">--  2</gadget>
<output>2</output>
2   x#+7==&gt; 2#+7 = 2+7= 
<gadget id="calculator">2+7</gadget>
<output>9</output>
9= 3*3.   Thus 3 is the smallest possible Prime Factor   2 cannot be the possible prime factor because --&gt; x# is always even since it is product of even numbers   Even +7 = Odd. Hence 2 cannot be prime factor of this result   ANSWER:3
<result>B</result>
x# is defined for every positive even integer x as the product of all even integers from 2 to x. What is the smallest possible prime factor of (x#+7)?