5'1 Monomials

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5.1 Monomials

• Objective
• To multiply and divide monomials
• To represent numbers in scientific notation
• To multiply and divide expressions written in
  scientific notation

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• Vocabulary
• Monomial- an expression that is a number, a
  variable, or the product of a number and one or
  more variables.
• examples
• not examples
• Constants- monomials that have no variables
• Coefficients- the numerical factor of the
  monomial
• Degree- the monomials sum of the exponents of
  its variables

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• Express each number in scientific notation.
• 1) 2,340,000 2) 0.00012

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• Simplify
• 3) 4)

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• Simplify
• 5) 6) 7)

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• Express each number in scientific and decimal
  notations.
• 8) 9)

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• 5.1 Assignment
• Page 259 (19-57) odd, 67, 70, 71, 72, 73, 75, 76,
  77, 78, 79
• Quiz tomorrow over vocabulary
• Give definition and example

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5.2 Polynomials

• Objective
• To add, subtract, and multiply polynomials

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• Vocabulary
• Like Terms- two monomials that are the same, or
  differ only by their numerical coefficients
• example 2xy 3xy
• Polynomial- is a monomial or a sum of monomials
• Trinomial- an expression with 3 unlike terms
• example 2xy 3xyz 7x
• Binomial- an expression with 2 unlike terms
• example

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• Determine whether or not each expression is a
  polynomial. Then state the degree of each
  polynomial.
• 1) 2)

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• Simplify
• 3) 4)

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• Simplify
• 5) 6)

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• Assignment 5.2
• Page 264 (19-59) odd, 66, 71, 72, 73, 74

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5.3 Dividing Polynomials

• Objective
• To divide polynomials using long division
• 2) To divide polynomials by binomials using
  synthetic division.

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• Simplify. (Dividing a polynomial by a monomial)
• 1) 2)

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• Simplify. (Dividing a polynomial by a binomial)
• 3) 4)

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Use synthetic division to solve.

• Rules to Use Synthetic
• The degree of the terms of the polynomial must be
  in descending order without any gaps.
• The divisor must be a binomial with a coefficient
  of one.

• 5)

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Use synthetic division to solve.

• Rules to Use Synthetic
• The degree of the terms of the polynomial must be
  in descending order without any gaps.
• The divisor must be a binomial with a coefficient
  of one.

• 6)

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• Assignment 5.3
• Page 271 (15-41) odd, 49, 50, 52, 53, 54, 55, 56,
  57

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5.4A Factoring

• Objective
• To factor polynomials
• To use factoring to simplify polynomial quotients

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• Factor completely. If you cant factor write
  prime.
• 1) 2)

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• Factor completely. If you cant factor write
  prime.
• 3) 4)

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• Factor completely. If you cant factor write
  prime.
• 5) 6)

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• Factor completely. If you cant factor write
  prime.
• 7) 8)

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• Assignment 5.4A
• Page 279 (18, 19, 21, 22, 23, 24, 27, 30, 31, 42,
  46, 47, 48, 49, 50, 69, 71, 72, 73)

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5.4B Factoring

• Objective
• To factor polynomials
• To use factoring to simplify polynomial quotients

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More Factoring MethodsGFC 1st if possible

• FOIL Method

• AC Method

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• Factor completely. Write prime if not possible.
  Use FOIL or AC Method.
• 1) 2)

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• Factor completely. Write prime if not possible.
  Use FOIL or AC Method.
• 3) 4)

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• Factor completely. Write prime if not possible.
  Use FOIL or AC Method.
• 5) 6)

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• 7) Show that 4 w is a factor of

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• 8) Show that 2 x is a factor of

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• Assignment 5.4B
• Page 279 (17, 20, 23, 25, 26, 28, 29, 32, 33, 34,
  35, 36, 37, 38, 39, 44, 45, 51, 63, 64, 66)

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5.1-5.4 Review
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• Unit 5 Quiz is worth 50 points
• Covers sections 5.1, 5.2, 5.3, 5.4A, 5.4B
• Study notes and hw
• Monomial Scientific Notation
• Polynomials Long Division
• Synthetic Division GCF
• Degree Difference of 2 Squares
• Negative Exponents Difference of 2 Cubes
• Multiplying Powers Sum of 2 Cubes
• Dividing Powers FOIL Method
• Power of a Power AC Method

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5.5 Roots of Real Numbers

• Objective
• To simplify radicals having various indices
• To use a calculator to estimate roots of numbers

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• Parts of a root
• Index Radical sign Name the parts of the
  roots below.
• Radicand

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• Find each root. Identify the index 1st.
• 1) 2)

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• Find each root. Identify the index 1st.
• 3) 4) 5)

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• Find each root. Identify the index 1st.
• 6) 7) 8)

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• Find each root. Identify the index 1st.
• 9) 10)

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• Use a calculator to find the value of each 3
  decimal places out.
• 11) 12) 13)

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• Assignment 5.5
• Page 285 (21-57) odd, 61, 63, 64, 65, 67, 68, 69,
  70

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5.6 Radical Expressions

• Objective
• To simplify radical expressions
• To rationalize the denominator of a fraction
  containing a radical expression
• To add, subtract, multiply, and divide radical
  expressions

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• Simplify.
• 1) 2)

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• Simplify.
• 3) 4)

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• Simplify.
• 5) 6)

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• Simplify.
• 7) 8)

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• Simplify.
• 9) 10)

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• Simplify.
• 11) 12)

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• Simplify. Use the conjugate.
• 13) 14)

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• Assignment 5.6
• Page 293 (23-59) odd, 68, 69, 70, 71, 73, 74, 75,
  76, 77

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5.7 Rational Exponents

• Objective
• To solve problems by identifying and achieving
  sub goals
• To write expressions with rational exponents in
  simplest radical form and vice versa
• To evaluate expressions in either exponential or
  radical form

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• Evaluate each expression. Show radical and
  exponent method.
• 1) 2)

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• Evaluate each expression. Show radical and
  exponent method.
• 3) 4)

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• Simplify each expression in exponential form.
• 5) 6) 7)

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• Simplify each expression in exponential form.
• 8) 9)

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• Simplify each expression in radical form.
• 10) 11)

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• Simplify each expression in radical form.
• 12) 13)

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• Assignment 5.7
• Page 300 (25-57) odd, leave answers in either
  exponential form or radical form
• 69, 70, 71, 72, 75, 78, 79, 80

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5.8 Solving Radical Equations and Inequalities

• Objective
• To solve equations and inequalities containing
  radicals.

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• Solve and check for extraneous solutions.
• 1) 2)

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• Solve and check for extraneous solutions.
• 3) 4)

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• Solve and check for extraneous solutions.
• 5) 6)

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• Solve and check for extraneous solutions.
• 7) 8)

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• Assignment 5.8
• Page 307 (15-41) odd, 56, 57, 58, 59, 61, 62, 63

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5.9 Complex Numbers

• Objective
• To simplify square roots containing negative
  radicands
• To solve quadratic equations that have pure
  imaginary solutions
• To add, subtract, and multiply complex numbers

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• Simplify.
• 1) 2) 3)

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• Simplify.
• 4) 5) 6)

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• Simplify.
• 7) 8) 9)

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• Solve and check solution.
• 10) 11)

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• Simplify.
• 12) (8 5i) (2 i) 13) (4 7i) (2 3i)

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• Simplify. Review
• 14) (4 2i)(3 5i) i ______
• ______

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• Assignment 5.9
• Page 314 (21 55) odd, 71, 73, 74, 76, 77, 78,
  79, 80, 81, 82

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5.10 Simplifying Expressions Containing Complex
Numbers

• Objective
• To simplify rational expressions containing
  complex numbers in the denominator

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• Find the conjugate of each complex numbers.
• 1) 10i 2) 7 i

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• Simplify
• 3) (15 3i)(15 3i) 4)

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• Simplify
• 5) 6)

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• Find the product of each complex number and its
  conjugate.
• 7) -2i 8) 4 6i

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• Find the multiplicative inverse of each complex
  number
• 9) 2 8i 10) x yi

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• Assignment 5.10
• Page 320 (17-45) odd, 49, 51, 53, 60, 61, 64, 65,
  66, 67, 68, 69

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Unit 5 ReviewExploring Polynomials and Radical
Expressions
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• Unit 5 Test is worth 100 points
• Covers sections 5.1, 5.2, 5.3, 5.4A, 5.4B, 5.5,
  5.6, 5.7, 5.8, 5.9, 5.10
• Study notes, hw, review sheet.

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• Items on the Test
• Monomial
• Polynomials
• Synthetic Division
• Degree
• Negative Exponents
• Multiplying Powers
• Dividing Powers
• Power of a Power
• Scientific Notation
• Long Division
• GCF
• Difference of 2 Squares
• Difference of 2 Cubes
• Sum of 2 Cubes
• FOIL Method
• AC Method

• Simplifying Radicals
• Add, Subtract, Multiply, and Divide Radicals
• Conjugate
• Radical Exponents
• Radical Equations and Inequalities
• Complex numbers (imaginary numbers)