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Intermediate Algebra Key Concepts

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Terms in this set (24)

  • What is an algebraic expression?
    An algebraic expression is a combination of variables, numbers, and operations without an equality sign.
  • Name the main sets of numbers used in algebra.
    The main sets are natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers.
  • What is the order of operations in algebra?
    The order is Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right).
  • State the distributive property.
    The distributive property states \(a(b + c) = ab + ac\).
  • What are the properties of real numbers?
    Properties include commutative, associative, distributive, identity, and inverse properties.
  • How do you solve a linear equation in one variable?
    Isolate the variable using inverse operations to get the variable alone on one side of the equation.
  • What is a formula in algebra?
    A formula is an equation that expresses a relationship between variables.
  • How do you solve linear inequalities?
    Solve like linear equations but reverse the inequality sign when multiplying or dividing by a negative number.
  • What is the slope of a line?
    Slope measures the steepness of a line and is calculated as rise over run: \(m = \frac{y_2 - y_1}{x_2 - x_1}\).
  • How do you graph a linear equation?
    Plot points that satisfy the equation and connect them with a straight line.
  • What is a function?
    A function assigns exactly one output for each input.
  • What is the standard form of a linear equation?
    Standard form is \(Ax + By = C\), where A, B, and C are constants.
  • How do you solve systems of linear equations by graphing?
    Graph both equations and find the point where the lines intersect.
  • What is the elimination method for solving systems?
    Add or subtract equations to eliminate one variable, then solve for the other.
  • What is the substitution method for solving systems?
    Solve one equation for a variable and substitute into the other equation.
  • Define an exponent.
    An exponent shows how many times a base is multiplied by itself.
  • State the product of powers property.
    When multiplying like bases, add exponents: \(a^m \cdot a^n = a^{m+n}\).
  • What is a polynomial?
    A polynomial is a sum of terms with variables raised to whole number exponents.
  • How do you multiply polynomials?
    Use the distributive property to multiply each term in one polynomial by each term in the other.
  • What is the greatest common factor (GCF)?
    The GCF is the largest factor shared by two or more terms.
  • How do you factor by grouping?
    Group terms with common factors and factor each group separately.
  • What is a trinomial?
    A polynomial with exactly three terms.
  • How do you factor trinomials?
    Find two numbers that multiply to the constant term and add to the middle coefficient, then factor accordingly.
  • How do you solve equations by factoring?
    Set the equation equal to zero, factor, then set each factor equal to zero and solve.