Final answer:
By performing long division, we find that 2x^2 + 3 is not a factor of 3x^3 - 7x^2 + 5x^2 - 3 as there is a non-zero remainder. The answer is B) No, it's not a factor.
Step-by-step explanation:
To determine if 2x^2 + 3 is a factor of 3x^3 - 7x^2 + 5x^2 - 3, we need to use long division. Before we start, let's simplify the polynomial by combining like terms, in this case, the x^2 terms. So, the polynomial simplifies to 3x^3 - 2x^2 - 3.
Now, we proceed with the long division:
- Divide the first term of the dividend, 3x^3, by the first term of the divisor, 2x^2, to get 3/2x.
- Multiply the entire divisor by 3/2x and subtract this from the dividend.
- Bring down the next term and repeat these steps until all terms have been used.
After performing these steps, you'll either end up with a remainder of zero, which means the divisor is a factor of the dividend, or with a non-zero remainder, meaning it's not a factor. If we perform this division, we find that there is a remainder, indicating that 2x^2 + 3 is not a factor of 3x^3 - 7x^2 + 5x^2 - 3. Therefore, the correct answer is B) No, it's not a factor.
Lastly, always review the result to ensure it is reasonable and that no errors have occurred during the division process.