Final answer:
To find the value of k for which the cubic polynomial 3x^3 - 3^2x^2 + kx + 5 is exactly divisible by (x - 1/2), we can use the Remainder Theorem.
Step-by-step explanation:
To find the value of k for which the cubic polynomial 3x3 - 32x2 + kx + 5 is exactly divisible by (x - 1/2), we can use the Remainder Theorem. According to the Remainder Theorem, if a polynomial f(x) is divided by (x - a), the remainder is zero when f(a) = 0. So, to find the value of k, we need to substitute x = 1/2 into the polynomial and set it equal to zero.
3(1/2)3 - (3/2)2(1/2) + k(1/2) + 5 = 0
Solving this equation will give us the value of k.