Polynomials

• What are the two methods to find the zeros of a polynomial?

  Factoring and quadratic formula
• What is the process of factoring a polynomial?

  • Break down the polynomial into factors
  • Set each factor equal to zero
  • Solve for $x$
• How do you factor the polynomial $x^{2} - 5x +$$6$?


  Find numbers that multiply to $6$ and add to $-5$
• What are the two numbers that multiply to $6$ and add to $-5$?


  -2 and -3
• What is the factored form of $x^{2} - 5x +$$6$?


  $(x - 2)(x - 3)$
• What do you do after factoring a polynomial?

  Set each factor equal to zero
• What are the zeros of $x^{2} - 5x +$$6$?


  2 and 3
• What is the quadratic formula?

  $x =$$\frac{ - b \pm \sqrt{b^{2} - 4ac}}{2a}$

  • Used for solving quadratic equations
  • $a, b, c$ are coefficients
• What is the standard form of a quadratic equation?

  $ax^{2} +$$bx +$$c =$$0$
• How do you identify coefficients in $6x^{2} - 7x - 3 =$$0$?


  $a =$$6, b =$$-7, c =$$-3$
• What is the first step in using the quadratic formula?

  Identify coefficients $a, b, c$
• What do you plug into the quadratic formula for $6x^{2} - 7x - 3 =$$0$?


  Values $6, -7, -3$
• What is the discriminant in the quadratic formula?

  $b^{2} - 4ac$
• What is the value of $x$ after plugging into the quadratic formula for $6x^{2} - 7x - 3 =$$0$?


  $x =$$\frac{7 \pm 11}{12}$
• What are the two possible values of $x$ from $6x^{2} - 7x - 3 =$$0$?


  $\frac{3}{2} \text{ and } -\frac{1}{3}$
• What are the advantages of factoring versus using the quadratic formula?

  • Factoring is quicker for simple quadratics
  • Quadratic formula works for all quadratics
• When should you use the quadratic formula?

  For polynomials that are hard to factor
• How do factoring and the quadratic formula compare in terms of complexity?

  Factoring is simpler; quadratic formula is universal