Determine the 5th term in the expansion of (x-3)11.

To find the 5th term in the expansion of (x-3)^11, we can use the binomial theorem, which states that any term in the expansion of (a+b)^n can be found using the formula:

T(r) = nCr * a^(n-r+1) * b^(r-1)

where:

• T(r) is the rth term
• nCr is "n choose r", a combination which can be calculated as n! / [(n-r)! * r!]
• a and b are the terms in the binomial (in this case, a=x and b=-3)
• n is the power to which the binomial is raised (in this case, 11)
• r is the term number

We want to find the 5th term, so r=5. Plugging in the values, we get:

T(5) = 11C5 * x^(11-5+1) * (-3)^(5-1) = 462 * x^7 * 81 = 37449x^7

So, the 5th term in the expansion of (x-3)^11 is 37449x^7.