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Algebra

Payton Kopp English

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Algebra

Factoring Introduction
- Greatest Common Factor
- Factoring by Grouping
  - 1.Factor out the GCF
    - 2. Make groups out of two terms. If the third term of the polynomial is subtracted before grouping, rewrite it as an addition by the additive inverse
      - 3. For each group of the two terms, determine the GCF
        4. Remove the GCF from each group
        5. If each group has a common polynomial factor, factor out. If not, return to step 2 and try a different grouping
        6. Verify that the factorization is correct.
        Toolkit B.1 Combining Algebraic Expressions Section 6.1 Working with Functions: Algebraic Operations
        A Monomial is an algebraic expression with one term
        A Binomial is an algebraic expression with two terms
        A Trinomial is an algebraic expression with three terms
        A Polynomial is the highest exponent. The exponents must be integers for an expression to be a polynomial
        Special Product formulas
        (A+B)(A-B)= A^2-B^2
        (A+B)^2= A^2+2AB+B^2
        (A-B)^2= A^2-AB+B^2
        Factoring Review
        Factoring out common factors
        Finding the greatest common factor (GCF) for the terms of the polynomial. The GCF is the largest factor that all terms have in common.
        (Optional) Rewrite each term as the product of the GCF and the remaining factor.
        Factor out the GCF from each term. Simplify the remaining factor if possible.
        Verify that the factorization is correct.
        S.A.M stands for Skip, Add, Multiply
        Guess and check method
        AC Method
        Special Factoring Formulas
        A^2+2AB+B^2= (A+B)^2
        A^2-2AB+B^2= (A-B)^2
        A^2-B^2 =(A+B)(A-B)
        Toolkit C.2 Solving Quadratic Functions
        Product Property of zero.
        Set equal to zero, factor completely set each factors equal to zero and solve.
        Square Root Property
        Complete the square
        Quadratic Formula
        Section 5.2 Quadratic Functions and their graphs
        Vertex form of a parabola
        Section 5.3 Maxima and Minima: Getting Info from a model
        Section 5.4 Quadratic Equations: Getting Info from a model
        Direct & Inverse Variation
        Multiplying & Dividing Rational Expressions
        To Multiply rational Expressions, Factor the numerators and denominators completely. Simplify by dividing out common factors in the numerator and the denominator. Multiply the remaining factors of the numerators together and multiply the remaining factors of the denominator together.
        To Divide rational expressions, invert the divisor and multiply.
        Rational Functions
        A Rational function is the quotient of two polynomials
        Simplifying Rational Expressions
        A rational expression is a fractional expression in which the numerator and denominator are both polynomials
        To simplify a rational expression, factor the numerator and the denominator completely and divide out any common factors using the following property of fractions.
        Adding & Subtracting Rational Expressions
        To add or subtract rationals expressions, first find a common denominator and then use the following properties of fractions
        Adding
        Subtracting