Final answer:
To simplify the given expression, combine like terms to obtain the simplified form x² + 4x + 3.
Step-by-step explanation:
The student is seeking to simplify an algebraic expression by combining like terms and subtracting polynomials. To find an expression with the fewest number of terms, we must perform operations keeping in mind to eliminate terms wherever possible.
Starting with (5x + 2x² + 6x - 4) - (3x + x² + 4x - 7), we combine like terms by addition or subtraction and group together to simplify:
Combine the x terms: (5x + 6x) - (3x + 4x) = 11x - 7x = 4x. Combine the x² terms: 2x² - x² = x². Combine the constant terms: -4 - (-7) = -4 + 7 = 3. The expression simplifies to: x² + 4x + 3. A simple check ensures this is reasonable.