Final answer:
The expression is simplified by combining like terms, resulting in -5x^3 + 4x^2 + 2x + 15 with four terms and a leading coefficient of -5. The answer (A) is correct.
Step-by-step explanation:
To simplify the algebra in the expression 7x^2 + 6 + 2x - 5x^3 + 9 - 3x^2, we start by combining like terms. We group all the terms that contain the same power of x:
- Combine the terms with x^2: 7x^2 - 3x^2 = 4x^2.
- There is only one term with x^3: -5x^3.
- Combine the constant terms: 6 + 9 = 15.
- There is also only one term with x: 2x.
Putting these together gives us a simplified expression: -5x^3 + 4x^2 + 2x + 15. The expression now has four terms, and the leading coefficient is -5, which is the coefficient of the highest power term x^3.
Thus, the correct answer is (A) 4 terms and leading coefficient -5.
Next, we should check if the answer is reasonable. The simplified expression should retain the same degree as the original and when each term is accounted for correctly, our simplification is indeed accurate.