Answer:
a = -1
g(2) = 3
Explanation:
Given polynomial:

The remainder theorem states that when a polynomial p(x) is divided by a linear polynomial (x - c), then the remainder is equal to p(c).
Therefore, if the polynomial g(t) is divided by (t + 2), then the remainder is equal to g(-2):

If the polynomial g(t) is divided by (t - 1), then the remainder is equal to g(1):

Given that the remainder (4a - 5) is three times the remainder (a - 2), then:

Therefore, the value of a = -1.
To find the value of g(2), substitute the found value of a = -1 into function g(t), then substitute t = 2 into the equation:


Therefore, the value of g(2) is:
