6.1%20-%20Polynomials

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6.1 - Polynomials

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• Monomial

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• Monomial 1 term

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• Monomial 1 term a variable

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• Monomial 1 term a variable, number times a
  variable

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• Monomial 1 term a variable, number times a
  variable, or multiple of numbers and variables.

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• Monomial 1 term a variable, number times a
  variable, or multiple of numbers and variables.
• Operations with Monomials

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• Monomial 1 term a variable, number times a
  variable, or multiple of numbers and variables.
• Operations with Monomials
• Ex. 1 Simplify x4x3

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• Monomial 1 term a variable, number times a
  variable, or multiple of numbers and variables.
• Operations with Monomials
• Ex. 1 Simplify x4x3

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• Monomial 1 term a variable, number times a
  variable, or multiple of numbers and variables.
• Operations with Monomials
• Ex. 1 Simplify x4x3
• xxxx

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• Monomial 1 term a variable, number times a
  variable, or multiple of numbers and variables.
• Operations with Monomials
• Ex. 1 Simplify x4x3
• xxxx

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• Monomial 1 term a variable, number times a
  variable, or multiple of numbers and variables.
• Operations with Monomials
• Ex. 1 Simplify x4x3
• xxxxxxx

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• Monomial 1 term a variable, number times a
  variable, or multiple of numbers and variables.
• Operations with Monomials
• Ex. 1 Simplify x4x3
• xxxxxxx

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• Monomial 1 term a variable, number times a
  variable, or multiple of numbers and variables.
• Operations with Monomials
• Ex. 1 Simplify x4x3
• xxxxxxx
• x7

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• Monomial 1 term a variable, number times a
  variable, or multiple of numbers and variables.
• Operations with Monomials
• Ex. 1 Simplify x4x3
• xxxxxxx
• x7
• Ex. 2 Simplify x5
• x3

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• Monomial 1 term a variable, number times a
  variable, or multiple of numbers and variables.
• Operations with Monomials
• Ex. 1 Simplify x4x3
• xxxxxxx
• x7
• Ex. 2 Simplify x5
• x3

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• Monomial 1 term a variable, number times a
  variable, or multiple of numbers and variables.
• Operations with Monomials
• Ex. 1 Simplify x4x3
• xxxxxxx
• x7
• Ex. 2 Simplify x5
• x3
• xxxxx

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• Monomial 1 term a variable, number times a
  variable, or multiple of numbers and variables.
• Operations with Monomials
• Ex. 1 Simplify x4x3
• xxxxxxx
• x7
• Ex. 2 Simplify x5
• x3
• xxxxx

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• Monomial 1 term a variable, number times a
  variable, or multiple of numbers and variables.
• Operations with Monomials
• Ex. 1 Simplify x4x3
• xxxxxxx
• x7
• Ex. 2 Simplify x5
• x3
• xxxxx
• xxx

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• Monomial 1 term a variable, number times a
  variable, or multiple of numbers and variables.
• Operations with Monomials
• Ex. 1 Simplify x4x3
• xxxxxxx
• x7
• Ex. 2 Simplify x5
• x3
• xxxxx
• xxx
• x2

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• Monomial 1 term a variable, number times a
  variable, or multiple of numbers and variables.
• Operations with Monomials
• Ex. 1 Simplify x4x3 OR x4x3
• xxxxxxx
• x7
• Ex. 2 Simplify x5
• x3
• xxxxx
• xxx
• x2

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• Monomial 1 term a variable, number times a
  variable, or multiple of numbers and variables.
• Operations with Monomials
• Ex. 1 Simplify x4x3 OR x4x3
• xxxxxxx x43
• x7
• Ex. 2 Simplify x5
• x3
• xxxxx
• xxx
• x2

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• Monomial 1 term a variable, number times a
  variable, or multiple of numbers and variables.
• Operations with Monomials
• Ex. 1 Simplify x4x3 OR x4x3
• xxxxxxx x43
• x7 x7
• Ex. 2 Simplify x5
• x3
• xxxxx
• xxx
• x2

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• Monomial 1 term a variable, number times a
  variable, or multiple of numbers and variables.
• Operations with Monomials
• Ex. 1 Simplify x4x3 OR x4x3
• xxxxxxx x43
• x7 x7
• Ex. 2 Simplify x5 x5
• x3 x3
• xxxxx
• xxx
• x2

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• Monomial 1 term a variable, number times a
  variable, or multiple of numbers and variables.
• Operations with Monomials
• Ex. 1 Simplify x4x3 OR x4x3
• xxxxxxx x43
• x7 x7
• Ex. 2 Simplify x5 x5
• x3 x3
• xxxxx x5-3
• xxx
• x2

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• Monomial 1 term a variable, number times a
  variable, or multiple of numbers and variables.
• Operations with Monomials
• Ex. 1 Simplify x4x3 OR x4x3
• xxxxxxx x43
• x7 x7
• Ex. 2 Simplify x5 x5
• x3 x3
• xxxxx x5-3
• xxx
• x2 x2

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• Ex. 3 Simplify (y6)3

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• Ex. 3 Simplify (y6)3

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• Ex. 3 Simplify (y6)3
• (y6)(y6)(y6)

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• Ex. 3 Simplify (y6)3
• (y6)(y6)(y6)
• y666

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• Ex. 3 Simplify (y6)3
• (y6)(y6)(y6)
• y666
• y18

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• Ex. 3 Simplify (y6)3 OR (y6)3
• (y6)(y6)(y6)
• y666
• y18

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• Ex. 3 Simplify (y6)3 OR (y6)3
• (y6)(y6)(y6) y63
• y666
• y18

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• Ex. 3 Simplify (y6)3 OR (y6)3
• (y6)(y6)(y6) y63
• y666 y18
• y18

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• Ex. 3 Simplify (y6)3 OR (y6)3
• (y6)(y6)(y6) y63
• y666 y18
• y18
• Ex. 4 Simplify (7x3y-5)(4xy3)

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• Ex. 3 Simplify (y6)3 OR (y6)3
• (y6)(y6)(y6) y63
• y666 y18
• y18
• Ex. 4 Simplify (7x3y-5)(4xy3)

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• Ex. 3 Simplify (y6)3 OR (y6)3
• (y6)(y6)(y6) y63
• y666 y18
• y18
• Ex. 4 Simplify (7x3y-5)(4xy3)
• (74)

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• Ex. 3 Simplify (y6)3 OR (y6)3
• (y6)(y6)(y6) y63
• y666 y18
• y18
• Ex. 4 Simplify (7x3y-5)(4xy3)
• (74)

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• Ex. 3 Simplify (y6)3 OR (y6)3
• (y6)(y6)(y6) y63
• y666 y18
• y18
• Ex. 4 Simplify (7x3y-5)(4xy3)
• (74)(x3x)

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• Ex. 3 Simplify (y6)3 OR (y6)3
• (y6)(y6)(y6) y63
• y666 y18
• y18
• Ex. 4 Simplify (7x3y-5)(4xy3)
• (74)(x3x)

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• Ex. 3 Simplify (y6)3 OR (y6)3
• (y6)(y6)(y6) y63
• y666 y18
• y18
• Ex. 4 Simplify (7x3y-5)(4xy3)
• (74)(x3x)(y3y-5)

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• Ex. 3 Simplify (y6)3 OR (y6)3
• (y6)(y6)(y6) y63
• y666 y18
• y18
• Ex. 4 Simplify (7x3y-5)(4xy3)
• (74)(x3x)(y3y-5)
• 28x4y-2

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• Ex. 3 Simplify (y6)3 OR (y6)3
• (y6)(y6)(y6) y63
• y666 y18
• y18
• Ex. 4 Simplify (7x3y-5)(4xy3)
• (74)(x3x)(y3y-5)
• 28x4y-2
• 28x4
• y2

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• Ex. 3 Simplify (y6)3 OR (y6)3
• (y6)(y6)(y6) y63
• y666 y18
• y18
• Ex. 4 Simplify (7x3y-5)(4xy3)
• (74)(x3x)(y3y-5)
• 28x4y-2
• 28x4
• y2
• Ex. 5 Simplify -5x3y3z4
• 20x3y7z4

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• Ex. 3 Simplify (y6)3 OR (y6)3
• (y6)(y6)(y6) y63
• y666 y18
• y18
• Ex. 4 Simplify (7x3y-5)(4xy3)
• (74)(x3x)(y3y-5)
• 28x4y-2
• 28x4
• y2
• Ex. 5 Simplify -5x3y3z4
• 20x3y7z4
• -5 x3-3 y3-7 z4-4
• 20

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• Ex. 3 Simplify (y6)3 OR (y6)3
• (y6)(y6)(y6) y63
• y666 y18
• y18
• Ex. 4 Simplify (7x3y-5)(4xy3)
• (74)(x3x)(y3y-5)
• 28x4y-2
• 28x4
• y2
• Ex. 5 Simplify -5x3y3z4
• 20x3y7z4
• -5 x3-3 y3-7 z4-4
• 20
• -¼x0y-4z0

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• Ex. 3 Simplify (y6)3 OR (y6)3
• (y6)(y6)(y6) y63
• y666 y18
• y18
• Ex. 4 Simplify (7x3y-5)(4xy3)
• (74)(x3x)(y3y-5)
• 28x4y-2
• 28x4
• y2
• Ex. 5 Simplify -5x3y3z4
• 20x3y7z4
• -5 x3-3 y3-7 z4-4
• 20
• -¼x0y-4z0
• -¼1y-41

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• Ex. 3 Simplify (y6)3 OR (y6)3
• (y6)(y6)(y6) y63
• y666 y18
• y18
• Ex. 4 Simplify (7x3y-5)(4xy3)
• (74)(x3x)(y3y-5)
• 28x4y-2
• 28x4
• y2
• Ex. 5 Simplify -5x3y3z4
• 20x3y7z4
• -5 x3-3 y3-7 z4-4
• 20
• -¼x0y-4z0
• -¼1y-41
• -1
• 4y4

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• Polynomials

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• Polynomials Expressions with more than 1
  term.

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• Polynomials Expressions with more than 1
  term.
• Degree

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• Polynomials Expressions with more than 1
  term.
• Degree highest combination of exponents on
  single term.

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• Polynomials Expressions with more than 1
  term.
• Degree highest combination of exponents on
  single term.
• Ex. 1 Determine the degree of the polynomial.

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• Polynomials Expressions with more than 1
  term.
• Degree highest combination of exponents on
  single term.
• Ex. 1 Determine the degree of the polynomial.
• x3y5 9x4

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• Polynomials Expressions with more than 1
  term.
• Degree highest combination of exponents on
  single term.
• Ex. 1 Determine the degree of the polynomial.
• x3y5 9x4

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• Polynomials Expressions with more than 1
  term.
• Degree highest combination of exponents on
  single term.
• Ex. 1 Determine the degree of the polynomial.
• x3y5 9x4
• degree 8

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• Operations with Polynomials

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• Operations with Polynomials
• Ex. 1 Simplify (5y 3y2) (-8y - 6y2)

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• Operations with Polynomials
• Ex. 1 Simplify (5y 3y2) (-8y - 6y2)
• 5y - 8y 3y2 - 6y2

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• Operations with Polynomials
• Ex. 1 Simplify (5y 3y2) (-8y - 6y2)
• 5y - 8y 3y2 - 6y2
• -3y - 3y2

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• Operations with Polynomials
• Ex. 1 Simplify (5y 3y2) (-8y - 6y2)
• 5y - 8y 3y2 - 6y2
• -3y - 3y2
• Ex. 2 Simplify (9r2 6r 16) (8r2 7r 10)

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• Operations with Polynomials
• Ex. 1 Simplify (5y 3y2) (-8y - 6y2)
• 5y - 8y 3y2 - 6y2
• -3y - 3y2
• Ex. 2 Simplify (9r2 6r 16) (8r2 7r 10)
• (9r2 6r 16) (-8r2 7r 10)

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• Operations with Polynomials
• Ex. 1 Simplify (5y 3y2) (-8y - 6y2)
• 5y - 8y 3y2 - 6y2
• -3y - 3y2
• Ex. 2 Simplify (9r2 6r 16) (8r2 7r 10)
• (9r2 6r 16) (-8r2 7r 10)
• 9r2 8r2 6r 7r 16 10

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• Operations with Polynomials
• Ex. 1 Simplify (5y 3y2) (-8y - 6y2)
• 5y - 8y 3y2 - 6y2
• -3y - 3y2
• Ex. 2 Simplify (9r2 6r 16) (8r2 7r 10)
• (9r2 6r 16) (-8r2 7r 10)
• 9r2 8r2 6r 7r 16 10
• r2 13r 6

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• Ex. 3 Simplify 4b(cb zd)

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• Ex. 3 Simplify 4b(cb zd)
• 4bcb 4bzd

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• Ex. 3 Simplify 4b(cb zd)
• 4bcb 4bzd
• 4b2c 4bdz

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• Ex. 3 Simplify 4b(cb zd)
• 4bcb 4bzd
• 4b2c 4bdz
• Ex. 4 Simplify (3x 8)(2x 6)

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• Ex. 3 Simplify 4b(cb zd)
• 4bcb 4bzd
• 4b2c 4bdz
• Ex. 4 Simplify (3x 8)(2x 6)
• 3x(2x 6) 8(2x 6)

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• Ex. 3 Simplify 4b(cb zd)
• 4bcb 4bzd
• 4b2c 4bdz
• Ex. 4 Simplify (3x 8)(2x 6)
• 3x(2x 6) 8(2x 6)
• 3x2x 3x6 82x 86

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• Ex. 3 Simplify 4b(cb zd)
• 4bcb 4bzd
• 4b2c 4bdz
• Ex. 4 Simplify (3x 8)(2x 6)
• 3x(2x 6) 8(2x 6)
• 3x2x 3x6 82x 86
• 32xx 36x 82x 86

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• Ex. 3 Simplify 4b(cb zd)
• 4bcb 4bzd
• 4b2c 4bdz
• Ex. 4 Simplify (3x 8)(2x 6)
• 3x(2x 6) 8(2x 6)
• 3x2x 3x6 82x 86
• 32xx 36x 82x 86
• 6x2 18x 16x 48

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• Ex. 3 Simplify 4b(cb zd)
• 4bcb 4bzd
• 4b2c 4bdz
• Ex. 4 Simplify (3x 8)(2x 6)
• 3x(2x 6) 8(2x 6)
• 3x2x 3x6 82x 86
• 32xx 36x 82x 86
• 6x2 18x 16x 48
• 6x2 34x 48