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    SECTION 4.1

    The power of the power rule:

    # 50

    The power of a Quotient rule:

    # 66

    Simplify, all variables represent nonzero real numbers:


    SECTION 4.2

    Negative Integral Exponents:


    The rules of Integral Exponents:




    Scientific Notation:



    Computations with Scientific Notation:


    SECTION 4.3

    Evaluating polynomials:



    Addition of Polynomials:


    Subtraction of Polynomials:


    SECTION 4.4

    Multiplying monomials


    Multiplying Polynomials




    SECTION 4.5

    The FOIL method:



    Multiplying Binomials Quickly


    SECTION 4.6

    Product of a Sum and a Difference:


    Miscellaneous: Find each product



    SECTION 4.7

    Dividing Monomials:



    Dividing a Polynomial by a Monomial


    Dividing a Polynomial by a Binomial: Write each expression in the form



    1. What is the difference between a term and a factor? Include detailed examples.

    2. When do you use the distributive property? Include detailed examples.

    3. What operations are associated with coefficients? Include detailed examples.

    4. What operations are associated with exponents? Include detailed examples


    1. When multiplying two polynomials, what fundamental property do you use repeatedly? Include algebraic examples (use variables).

    2. When working with exponents, is there any difference in operations if the exponents are whole numbers or fractions? Include algebraic examples (use variables).

    3. In what sense do exponentials and radicals behave exactly the same way?Include algebraic examples (use variables).

    4. Explain how division of real numbers corresponds with division of polynomials. Include algebraic examples (use variables).


    98. Area of a parallelogram. Find a trinomial A(x) that represents the area of a parallelogram whose base is meters and whose height is meters. Find A(3)

    114. Diameter of a circle. If the diameter of a circle is
    meters, then what is its radius?

    94. Perimeter of a rectangle. The width of a rectangular playground
    is feet, and the length is feet. Write a
    polynomial P(x) that represents the perimeter and then
    evaluate this perimeter polynomial if x is 4 feet.

    78. Swimming space. The length of a rectangular swimming
    pool is meters, and the width is meters. Write
    a polynomial A(x) that represents the area. Find A(5).

    96. Compounded semiannually. P dollars is invested at annual
    interest rate r for 1 year. If the interest is compounded
    semiannually, then the polynomial represents the
    value of the investment after 1 year. Rewrite this expression
    without parentheses. Evaluate the polynomial if and r = 10%

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