Polynomials

• What are the three main components of a polynomial term?

  Variable, coefficient, exponent
• What do exponents in a polynomial indicate?

  How many times to multiply
• Match the type of polynomial with its number of terms:

  Monomial ↔️ 1

  Binomial ↔️ 2

  Trinomial ↔️ 3
• What is the result of subtracting $(2x^{2} - x +$$3)$ from $(3x^{2} +$$2x - 5)$?


  $x^{2} +$$3x - 8$
• Steps to add two polynomials:

  1️⃣ Combine like terms

  2️⃣ Add the coefficients of like terms
• What is the result of dividing $(2x^{2} +$$5x - 3)$ by $(x + 3)$?


  $2x - 1$
• What does it mean to factorize a polynomial?

  Break it into simpler expressions
• Match the factoring method with its example:

  Common Factor ↔️ $4x^{2} +$$8x =$$4x(x + 2)$

  Difference of Squares ↔️ $x^{2} - 9 =$$(x + 3)(x - 3)$

  Perfect Square Trinomial ↔️ $x^{2} +$$6x +$$9 =$$(x + 3)^{2}$

  Grouping ↔️ $ax +$$ay +$$bx +$$by =$$(a + b)(x + y)$
• What is the factored form of the perfect square trinomial $x^{2} +$$6x +$$9$?


  $(x + 3)^{2}$
• Steps to solve a polynomial equation using factoring and the zero product property:

  1️⃣ Factor the polynomial

  2️⃣ Set each factor equal to zero

  3️⃣ Solve for x
• What are the solutions to the equation $x^{2} +$$4x - 5 =$$0$?


  $x =$$- 5$ and $x =$$1$