Algebra Basics

Algebra

• Definition: Algebra is a branch of mathematics that deals with the study of variables and their relationships, often expressed through the use of symbols, equations, and functions.
• Equations: An equation is a statement that says two expressions are equal, often denoted by the "=" symbol. Examples: 2x + 3 = 5, x^2 - 4 = 0.
• Variables: A variable is a letter or symbol that represents a value that can change. Examples: x, y, z.
• Constants: A constant is a value that does not change. Examples: 2, 5, -3.

Polynomials

• Definition: A polynomial is an expression consisting of variables and coefficients combined using only addition, subtraction, and multiplication.
• Examples: 3x^2 + 2x - 4, x^3 - 2x^2 - x + 1, 2x - 5.
• Degree: The degree of a polynomial is the highest power of the variable. Examples: 3x^2 + 2x - 4 has a degree of 2, x^3 - 2x^2 - x + 1 has a degree of 3.
• Terms: A term is a part of a polynomial separated by addition or subtraction. Examples: 3x^2, 2x, -4 are terms in the polynomial 3x^2 + 2x - 4.
• Coefficients: A coefficient is a number multiplied by a variable in a polynomial. Examples: 3 is the coefficient of x^2, 2 is the coefficient of x in the polynomial 3x^2 + 2x - 4.
• Like Terms: Like terms are terms with the same variable and exponent. Examples: 2x and 3x are like terms, x^2 and 2x^2 are like terms.
• Adding and Subtracting Polynomials: To add or subtract polynomials, combine like terms. Example: (2x^2 + 3x - 1) + (x^2 - 2x - 3) = 3x^2 + x - 4.

Algebra

• Algebra is a branch of mathematics that deals with the study of variables and their relationships.
• Variables are letters or symbols that represent values that can change.
• Constants are values that do not change.

Equations

• An equation is a statement that says two expressions are equal.
• Equations are often denoted by the "=" symbol.
• Examples of equations include 2x + 3 = 5 and x^2 - 4 = 0.

Polynomials

• A polynomial is an expression consisting of variables and coefficients combined using only addition, subtraction, and multiplication.
• Examples of polynomials include 3x^2 + 2x - 4, x^3 - 2x^2 - x + 1, and 2x - 5.
• The degree of a polynomial is the highest power of the variable.
• Examples of degrees include 2 for 3x^2 + 2x - 4 and 3 for x^3 - 2x^2 - x + 1.

Terms and Coefficients

• A term is a part of a polynomial separated by addition or subtraction.
• Examples of terms include 3x^2, 2x, and -4 in the polynomial 3x^2 + 2x - 4.
• A coefficient is a number multiplied by a variable in a polynomial.
• Examples of coefficients include 3 for x^2 and 2 for x in the polynomial 3x^2 + 2x - 4.

Like Terms and Operations

• Like terms are terms with the same variable and exponent.
• Examples of like terms include 2x and 3x, as well as x^2 and 2x^2.
• To add or subtract polynomials, combine like terms.
• Example: (2x^2 + 3x - 1) + (x^2 - 2x - 3) = 3x^2 + x - 4.