Equivalent expressions of polynomials

Lessons

• Introduction
  a)

  What is a polynomial?

  • Review on Variables, Coefficients, and Expressions
  • What are Monomials, Binomials, and Trinomials?
  • What are the Degree, Leading Term, and Constant term of a polynomial?
  • Name polynomials based on degree: Quadratic, Cubic, Quartic, Quintic, etc.
  
  
  b)

  How to find the degree of a polynomial?
  
  

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• 1.
  Identify the coefficient and the number of variables for each expression.
  a)

  $8x$
  
  
  b)

  $7{x^2}y$
  
  
  c)

  $- ab$
  
  

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• 2.
  Find the like terms.
  a)

  $3x$       $7y$       $50x$       $x$       $23{x^2}$
  
  
  b)

  $73{a^2}$       $\frac{1}{3}a$       $3{b^2}$       $0.3{c^{}}$       $3{a^2}b$
  
  
  c)

  $15y$       $- 23y$       $13{y^2}z$       $- 10y$       ${x^2}y$
  
  

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• 3.
  Combine like terms.
  a)

  $x^3 + x^5 + x^3$
  
  
  b)

  ${y^2} + {y^5} + 5{y^2} + x + {x^2} + x$
  
  
  c)

  ${z^3} - {z^3} + {z^2} + 2{x^5} - 4{y^3} + 3{z^2}$
  
  
  d)

  $x^2 + z^2 + 3x^2 - z^2 - 4x^2$
  
  
  e)

  ${z^2} + 3z + 4{z^3} - {3^4} - {z^5}$
  
  
  f)

  $5{y^2} + 4 - 6y + {y^2} - 3 + y$
  
  

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• 4.
  4. Write an equivalent expression with seven terms for each polynomial.
  a)

  ${x^2} + 2x + 3$
  
  
  b)

  $- {y^2} - 3{y^3} - x$
  
  
  c)

  $5x - 3y + 6xy$
  
  

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