Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial :`t^2-3,2t^4+3t^3-2t^2-9t-12`

Explanation

To determine whether the polynomial \( t^2 - 3 \) is a factor of the polynomial \( 2t^4 + 3t^3 - 2t^2 - 9t - 12 \), we will perform polynomial long division.

### Step-by-Step Solution:

1. **Set Up the Division**: We will divide \( 2t^4 + 3t^3 - 2t^2 - 9t - 12 \) by \( t^2 - 3 \).

2. **Divide the Leading Terms**:
- Divide the leading term of the dividend \( 2t^4 \) by the leading term of the divisor \( t^2 \):
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