Polynomials

• What are the components of a polynomial?

  Variables, constants, and exponents
• What is a polynomial?

  An expression with variables and constants
• What are constants in a polynomial?

  Numbers like $3, 2, -5$
• What are exponents in a polynomial?

  Powers to which variables are raised
• What are variables in a polynomial?

  Letters representing unknown values
• What is a single variable polynomial?

  $3x^{2} +$$2x - 5$
• What is a polynomial in multiple variables?

  $2xy +$$3x - 4y +$$1$
• What is a constant polynomial?

  $7$
• What is a linear polynomial?

  $5x - 2$
• What is a quadratic polynomial?

  $x^{2} +$$4x +$$3$
• How do you find the degree of a polynomial?

  Look for the highest exponent of variable terms
• What is the degree of $3x^{2} +$$5x - 2$?


  $2$
• What is the degree of $x^{3} - 4x^{2} +$$7x +$$1$?


  $3$
• What is the degree of a constant polynomial?

  $0$
• What is a monomial?

  A polynomial with one term
• What is a binomial?

  A polynomial with two terms
• What is a trinomial?

  A polynomial with three terms
• What is a polynomial?

  A polynomial with four or more terms
• What are the steps to add and subtract polynomials?

  1. Identify like terms
  2. Combine the coefficients
  3. Keep the variable and exponent the same
  4. Write the simplified polynomial
• How do you add the polynomials $(2x^{2} +$$3x - 1)$ and $(x^{2} - 2x +$$4)$?


  Combine like terms to get $3x^{2} +$$x +$$3$
• What are the key differences in adding and subtracting polynomials?

  • Addition: Add the coefficients of like terms
  • Subtraction: Subtract the coefficients of like terms
• How do you multiply the polynomials $(x + 2)(2x - 3)$ using the Distributive Property?


  Result is $2x^{2} +$$x - 6$
• How do you subtract the polynomials $(4y^{2} +$$5y - 3)$ and $(y^{2} +$$2y - 1)$?


  Combine like terms to get $3y^{2} +$$3y - 2$
• How do you multiply the binomials $(x + 4)(x + 1)$ using the FOIL method?


  Result is $x^{2} +$$5x +$$4$
• What are the key differences between the Distributive Property and FOIL method?

  • Distributive Property: General case for any polynomials
  • FOIL Method: Specifically for multiplying two binomials
• What are the steps to multiply polynomials?

  1. Distribute each term from the first polynomial to each term in the second
  2. Combine like terms
  3. Simplify the expression