2.2.2 Solving quadratic equations by factorization

• What is the highest power of 'x' in a quadratic equation?

  2
• What is the second step in completing the square after making the x² coefficient equal to 1?

  Halve the coefficient of x
• What does the variable 'a' represent in the standard form of a quadratic equation?

  Coefficient of x²
• Steps involved in completing the square method

  1️⃣ Make x² coefficient equal to 1

  2️⃣ Halve the coefficient of x

  3️⃣ Square the result

  4️⃣ Add and subtract the result
• What are the factors of a in the equation x² + 5x + 6 = 0?

  1 and 1
• What is the value of the expression 1x in the image?

  $1x$
• What is the missing value in the bottom right cell of the grid?


  ??
• In the factorization method, the middle term 'bx' is rewritten as two terms that add up to b and multiply to ac.


  True
• The first step in completing the square is to ensure the coefficient of x² is 1.


  True
• What is the first step in completing the square for $x^{2} +$$6x +$$5$?


  $x^{2} +$$6x$
• The result of squaring and adding/subtracting the halved coefficient of x completes the perfect square form.


  True
• One solution for x in the equation x² + 5x + 6 = 0 is -2.

  True
• What is the other solution for x in the equation x² + 5x + 6 = 0?

  -3
• If both sides of the equation are equal after simplification, the solution is correct.


  True
• What is the variable represented by the symbol 'x' in the image?


  x
• Match the value of the discriminant with the number of solutions:

  Positive discriminant ↔️ Two solutions

  Zero discriminant ↔️ One solution

  Negative discriminant ↔️ No real solutions
• What is the value of the expression x^2 in the image?

  $x^2$
• What type of number is represented by 'c' in a quadratic equation?

  Constant
• The discriminant $b^{2} - 4ac$ determines the number of real solutions of the quadratic equation


  True
• What is the final completed square form for $x^{2} +$$6x +$$5$?


  $(x + 3)^{2} - 4$
• In the quadratic equation 2x² + 5x - 3 = 0, the value of 'a' is 2.

  True
• What happens to the number of real solutions when the discriminant is negative?

  No real solutions
• What is the relationship between the expressions in the image?

  • The expressions represent a multiplication problem
  • The expressions are arranged in a grid format
  • The values in the grid represent the different terms in the multiplication problem
• Factorization is most effective when the quadratic equation is easily factorizable.


  True
• What are the solutions to the equation $x^{2} +$$5x +$$6 =$$0$?


  $x =$$- 2$ and $x =$$- 3$
• How does the "Divide both sides by a" step help simplify the equation?

  It removes the factor of a from the equation, making it easier to solve
• What are the key steps in the process described in the image?

  Key Steps:

  1. Factor a from the "x" terms
  2. Create a perfect square within the parentheses and add equivalent terms on both sides of the equation
  3. Divide both sides by a
  4. Take the square root
  5. Subtract b/2a and re-write radical
• What is the third step in the factorization method after rewriting the equation?

  Split into linear equations
• Why is the step of "Creating a perfect square within the parentheses and adding equivalent terms on both sides of the equation" important?

  To simplify the equation and make it easier to solve
• How do you re-write the LHS (left-hand side) of the equation?

  • Rewrite the LHS as: $a(x + \frac{b}{2a})^2$
• Squaring half of 6 results in 9.


  True
• Both $x =$$- 2$ and $x =$$- 3$ are correct solutions to the equation $x^{2} +$$5x +$$6 =$$0$.


  True
• The quadratic formula is derived from the standard quadratic equation $ax^{2} +$$bx +$$c =$$0$


  True
• What is the formula used to "Subtract \frac{b}{2a} and re-write radical"?

  $x =$$\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
• What is the factorization method used for?

  Solving quadratic equations
• What is the purpose of completing the square in mathematics?

  Create a perfect square
• Steps to solve the equation x² + 5x + 6 = 0 using the factorization method

  1️⃣ Find the factors of a and c

  2️⃣ Rewrite the equation

  3️⃣ Split into linear equations

  4️⃣ Solve for x
• How is the middle term 5x rewritten in the equation x² + 5x + 6 = 0?

  2x + 3x
• What is the first step in the process described in the image?

  Factor a from the "x" terms
• Completing the square or the quadratic formula are less efficient methods for solving $x^{2} +$$5x +$$6 =$$0$ compared to factorization.


  True