Test Review

1
Test Review

• Chapter 10 - Polynomials

2
Format for Next 2 Days

• Monday we will review the first half of the
  topics on the test. For homework you will
  complete the first half of the practice test.
• Tuesday we will answer questions on first half,
  then cover the second half of the topics on the
  test. For homework you will complete the second
  half of the practice test study.

3
Descending Order

• Descending Order means to rearrange the
  polynomial into decreasing powers of x (from
  highest to lowest)
• x - 3x4 x2 - 6

4
Descending Order

• Descending Order means to rearrange the
  polynomial into decreasing powers of x (from
  highest to lowest)
• x - 3x4 x2 6
• Whats the largest power of x?

5
Descending Order

• Descending Order means to rearrange the
  polynomial into decreasing powers of x (from
  highest to lowest)
• x - 3x4 x2 6
• Whats the largest power of x?
• Start with x4 and work down to constant
• Remember to keep the signs!

6
Descending Order

• Descending Order means to rearrange the
  polynomial into decreasing powers of x (from
  highest to lowest)
• x - 3x4 x2 6
• Whats the largest power of x?
• Start with x4 and work down to constant
• Remember to keep the signs!
• -3x4 x2 x - 6

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Degree Leading Coefficient

• Term a grouping of numbers and exponents
  connected via multiplication/division. Terms are
  separated by addition/subtraction.
• Degree is the highest exponent in any single term
• Leading Coefficient is the coefficient of the
  term containing the highest degree

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Name the number of terms, degree, and leading
coefficient

• 4x x3 8x4 5

9
Name the number of terms, degree, and leading
coefficient

• 4x x3 8x4 5

Term 1
Term 2
Term 3
Term 4
10
Name the number of terms, degree, and leading
coefficient

• 4x x3 8x4 5

Term 1
Term 2
Term 3
Term 4
4 Terms!
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Name the number of terms, degree, and leading
coefficient

• 4x x3 8x4 5

4 is the highest exponent, so the degree of the
polynomial is 4!
12
Name the number of terms, degree, and leading
coefficient

• 4x x3 8x4 5

8x4 is the term with the highest degree, so its
coefficient is the Leading Coefficient.The
Leading Coefficient is 8!
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Classifying Polynomials

• By Degree0- Constant1- Linear2- Quadratic

• By Number of Terms1- Monomial2- Binomial3-
  Trinomial

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Classifying Polynomials

• By Degree0- Constant1- Linear2- Quadratic

• By Number of Terms1- Monomial2- Binomial3-
  Trinomial

3x - 4 5x2 6x2 - x 4
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Classifying Polynomials

• By Degree0- Constant1- Linear2- Quadratic

• By Number of Terms1- Monomial2- Binomial3-
  Trinomial

3x - 4 5x2 6x2 - x 4 Linear
Binomial Quadratic Monomial Quadratic Trinomial
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Adding Polynomials

• You add polynomials by combining like terms.
• Find the highest degree and work your way down to
  the constant term
• (4x5 3x2 5) (x2 2x5 9)

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Adding Polynomials

• You add polynomials by combining like terms.
• Find the highest degree and work your way down to
  the constant term
• (4x5 3x2 5) (x2 2x5 9)
• 2x5

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Adding Polynomials

• You add polynomials by combining like terms.
• Find the highest degree and work your way down to
  the constant term
• (4x5 3x2 5) (x2 2x5 9)
• 2x5 - 2x2

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Adding Polynomials

• You add polynomials by combining like terms.
• Find the highest degree and work your way down to
  the constant term
• (4x5 3x2 5) (x2 2x5 9)
• 2x5 - 2x2 - 4

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Subtracting Polynomials

• First you change the subtracted term by flipping
  the signs
• Then you add the polynomials by combining like
  terms.
• Find the highest degree and work your way down to
  the constant term
• (4x4 3x2 5) - (x2 2x5 9)

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Subtracting Polynomials

• First you change the subtracted term by flipping
  the signs
• Then you add the polynomials by combining like
  terms.
• Find the highest degree and work your way down to
  the constant term
• (4x4 3x2 5) (-x2 2x5 9)

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Subtracting Polynomials

• First you change the subtracted term by flipping
  the signs
• Then you add the polynomials by combining like
  terms.
• Find the highest degree and work your way down to
  the constant term
• (4x4 3x2 5) (-x2 2x5 9)
• 2x5

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Subtracting Polynomials

• First you change the subtracted term by flipping
  the signs
• Then you add the polynomials by combining like
  terms.
• Find the highest degree and work your way down to
  the constant term
• (4x4 3x2 5) (-x2 2x5 9)
• 2x5 4x4

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Subtracting Polynomials

• First you change the subtracted term by flipping
  the signs
• Then you add the polynomials by combining like
  terms.
• Find the highest degree and work your way down to
  the constant term
• (4x4 3x2 5) (-x2 2x5 9)
• 2x5 4x4 4x2

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Subtracting Polynomials

• First you change the subtracted term by flipping
  the signs
• Then you add the polynomials by combining like
  terms.
• Find the highest degree and work your way down to
  the constant term
• (4x4 3x2 5) (-x2 2x5 9)
• 2x5 4x4 4x2 14

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End of Day One!

• For homework tonight, complete the first half of
  the practice test!
• Be prepared to ask any final questions about the
  test materials tomorrow (even the stuff we
  havent covered yet)

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Test Review

• DAY 2

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Format for Next 2 Days

• Monday we will review the first half of the
  topics on the test. For homework you will
  complete the first half of the practice test.
• Tuesday we will answer questions on first half,
  then cover the second half of the topics on the
  test. For homework you will complete the second
  half of the practice test study.

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Multiplying Monomial x Polyomial

• Use the distributive property to multiply each
  term of the polynomial by the binomial
• 3x2 (-2x3 4x2 8x 7)

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Multiplying Monomial x Polynomial

• Use the distributive property to multiply each
  term of the polynomial by the binomial
• 3x2 (-2x3 4x2 8x 7)
• -6x5 12x4 24x3 21x2

31
Multiplying Monomial x Polynomial

• Use the distributive property to multiply each
  term of the polynomial by the binomial
• 3x2 (-2x3 4x2 8x 7)
• -6x5 12x4 24x3 21x2

32
Multiplying Monomial x Polynomial

• Use the distributive property to multiply each
  term of the polynomial by the binomial
• 3x2 (-2x3 4x2 8x 7)
• -6x5 12x4 24x3 21x2

33
Multiplying Monomial x Polynomial

• Use the distributive property to multiply each
  term of the polynomial by the binomial
• 3x2 (-2x3 4x2 8x 7)
• -6x5 12x4 24x3 21x2

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FOIL

• FOIL Stands for First, Outer, Inner, Last
• It tells you what terms need to be multiplied
• (4x 5) (-2x 1)

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FOIL

• FOIL Stands for First, Outer, Inner, Last
• It tells you what terms need to be multiplied
• (4x 5) (-2x 1)
• -8x2 4x 10x 5

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FOIL

• FOIL Stands for First, Outer, Inner, Last
• It tells you what terms need to be multiplied
• (4x 5) (-2x 1)
• -8x2 4x 10x 5

37
FOIL

• FOIL Stands for First, Outer, Inner, Last
• It tells you what terms need to be multiplied
• (4x 5) (-2x 1)
• -8x2 4x 10x 5

38
FOIL

• FOIL Stands for First, Outer, Inner, Last
• It tells you what terms need to be multiplied
• (4x 5) (-2x 1)
• -8x2 4x 10x 5

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FOIL

• FOIL Stands for First, Outer, Inner, Last
• It tells you what terms need to be multiplied
• (4x 5) (-2x 1)
• -8x2 4x 10x 5
• -8x2 6x 5

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Special Patterns

• Sum and Difference
• (ab)(a-b) a2 b2

• Square of a binomial
• (ab)2 a2 2ab b2

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Special Patterns

• Sum and Difference
• (ab)(a-b) a2 b2
• (2x 8) (2x 8)

• Square of a binomial
• (ab)2 a2 2ab b2

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Special Patterns

• Sum and Difference
• (ab)(a-b) a2 b2
• (2x 8) (2x 8)
• 4x2 - 64

• Square of a binomial
• (ab)2 a2 2ab b2

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Special Patterns

• Sum and Difference
• (ab)(a-b) a2 b2
• (2x 8) (2x 8)
• 4x2 - 64

• Square of a binomial
• (ab)2 a2 2ab b2
• (2x 8)2

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Special Patterns

• Sum and Difference
• (ab)(a-b) a2 b2
• (2x 8) (2x 8)
• 4x2 - 64

• Square of a binomial
• (ab)2 a2 2ab b2
• (2x 8)2
• 4x2 32x 64

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End of Day Two!

• For homework tonight, complete the Second half of
  the practice test!
• Go back through the entire practice test and
  check your work make sure you know how to do
  every problem!
• Get a good nights rest, and eat breakfast! You
  would be surprised.