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The power of the power rule:
The power of a Quotient rule:
Simplify, all variables represent nonzero real numbers:
Negative Integral Exponents:
The rules of Integral Exponents:
Computations with Scientific Notation:
Addition of Polynomials:
Subtraction of Polynomials:
The FOIL method:
Multiplying Binomials Quickly
Product of a Sum and a Difference:
Miscellaneous: Find each product
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%
This posting contains the solution to the given problems.