1. The problem is to understand what "all of polynomials" means in algebra. 2. Polynomials are expressions consisting of variables and coefficients combined using addition, subtraction, multiplication, and non-negative integer exponents of variables. 3. The general form of a polynomial in one variable $x$ is: $$P(x) = a_n x^n + a_{n-1} x^{n-1} + \cdots + a_1 x + a_0$$ where $n$ is a non-negative integer, $a_n, a_{n-1}, \ldots, a_0$ are constants called coefficients, and $a_n \neq 0$. 4. Important rules: - The degree of the polynomial is the highest power $n$ with a non-zero coefficient. - Polynomials can be added, subtracted, and multiplied to form new polynomials. - Division of polynomials may not always result in a polynomial. 5. Examples: - $3x^2 + 2x - 5$ is a polynomial of degree 2. - $7$ is a polynomial of degree 0 (constant polynomial). 6. Polynomials are fundamental in algebra and are used to model many real-world problems. Final answer: Polynomials are algebraic expressions with variables raised to non-negative integer powers and combined with coefficients using addition, subtraction, and multiplication.