Hellllo, can I please get some help with the following here? I can't seem to figure out what approach we're supposed to use.. thank you!!
9a) Find what powers of the following are a divisor of 10!
i. 2
ii. 10
10b) Find the term independent of x in: (2x3 - 1/x)12
One way you could do it is find the prime factors of the number first ie 2 for i) and 2*5 for ii) and then look for multiples of this number in 10!
Multiples of 2 in 10! are 2,4,6,8,10 and the prime factors of these numbers are 2 , 2*2 , 2*3 , 2*2*2 , 5*2. So 10 is divisible by 2^8. So powers of 2^(0 to 8 ) are divisors
ii) is easier, 10 is 2*5, 5 is a factor of 5 and 10 while 2 is a factor of more numbers than that so 10^(0 to 2) are factors. 10^0 and 2^0 may not be considered divisors though
Note: I don't know what you're expected to do for this question just thought I'd give a solution, even if it isn't what they want hopefully it'll help!