Check whether the polynomial `q(t)=4t^3+4t^2-t-1`is a multiple of `2t+1`

Explanation

To determine whether the polynomial \( q(t) = 4t^3 + 4t^2 - t - 1 \) is a multiple of \( 2t + 1 \), we can use the Remainder Theorem. According to the theorem, if a polynomial \( f(t) \) is divided by \( t - r \), the remainder of that division is \( f(r) \). If \( f(r) = 0 \), then \( f(t) \) is a multiple of \( t - r \).

### Step-by-Step Solution:

1. **Identify the value of \( t \)**:
We need to find the value of \( t \) that makes \( 2t + 1 = 0 \).
\[
2t + 1 = 0 \implies 2t = -1 \implies t = -\frac{1}{2}
...