Chapter 1
Numbers and Operations
Course: Gace Middle Grades Math 4 8 704
Subject: Gace Middle Grades Math 4 8 704
Chapter: Algebra
1. Adds, subtracts, and multiplies linear and quadratic polynomials, including polynomials with rational coefficients
Polynomials are sums of terms that include constants and variables raised to non-negative integer exponents. A linear polynomial has the form ax + b (degree 1), while a quadratic has the form ax² + bx + c (degree 2).
When adding and subtracting polynomials, like terms (terms with the same variables raised to the same powers) are combined.
Example: (3x² + 4x – 7) + (2x² – 5x + 3) = (3x² + 2x²) + (4x – 5x) + (–7 + 3) = 5x² – x – 4.
Multiplication requires distributing each term across the other polynomial. Example: (x + 3)(x – 2) = x(x – 2) + 3(x – 2) = x² – 2x + 3x – 6 = x² + x – 6.