Final answer:
To simplify the given polynomial expression (3x^2 - x - 7) - (5x^2 - 4x - 2) + (x + 3)(x + 2), we need to perform the operations within the parentheses first. By simplifying each term and combining like terms, the simplified expression is -2x^2 - 4x - 3.
Step-by-step explanation:
To simplify the given polynomial expression, we need to perform the operations within the parentheses first. By simplifying each term, we get:
(3x^2 - x - 7) - (5x^2 - 4x - 2) + (x + 3)(x + 2)
Expanding the last term using the distributive property, we have:
(3x^2 - x - 7) - (5x^2 - 4x - 2) + x^2 + 5x + 6
Combining like terms, we get:
-2x^2 - 4x - 3
The simplified polynomial expression is -2x^2 - 4x - 3, which is a quadratic polynomial with a degree of 2.