Factorising harder quadratics

• What is the form of the quadratic equation discussed?

  ax² + bx + c
• How do we factorize the quadratic x² + 7x + 12?

  Find two numbers that multiply to 12 and add to 7
• What two numbers multiply to 12 and add to 7?

  3 and 4
• What is the result of expanding (x + 3)(x + 4)?

  x² + 7x + 12
• How do we expand and simplify (2x + 3)(x + 5)?

  Multiply each term in the first bracket by each term in the second
• What is the result of expanding (2x + 3)(x + 5)?

  2x² + 13x + 15
• Why can't we use the same method for factorizing 2x² + 13x + 15?

  Because the numbers don't add to 13
• What is the product of a and c in the factorization process?

  It helps find two numbers that multiply to ac
• What two numbers multiply to 30 and add to 13?

  3 and 10
• How do we factorize 2x² + 13x + 15 using 3 and 10?

  Use 2x and x, then simplify
• What is the factorization of 2x² + 13x + 15?

  (2x + 3)(x + 5)
• How do we factorize 5n² + 23n + 60?

  Find two numbers that multiply to 60 and add to 23
• What two numbers multiply to 60 and add to 23?

  3 and 20
• How do we factorize 3x² + 10x + 24?

  Find two numbers that multiply to 24 and add to 10
• What two numbers multiply to 24 and add to 10?

  4 and 6
• How do we factorize 3a² + 5a - 6?

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

  6 and -1
• How do we factorize 2x² + 13x + 15 with negatives?

  Use the same method but consider signs
• What is the factorization of 2x² + 13x + 15 with negatives?

  (2x - 6)(x - 7)
• What is the process for factorizing 4m² + 24m + 35?

  Find two numbers that multiply to 140 and add to 24
• What two numbers multiply to 140 and add to 24?

  10 and 14
• How do we simplify the factorization of 4m² + 24m + 35?

  Divide one of the numbers by 4
• What are the steps to factorizing a quadratic equation?

  1. Identify the coefficients a, b, and c.
  2. Calculate a times c.
  3. Find two numbers that multiply to ac and add to b.
  4. Rewrite the middle term using these numbers.
  5. Factor by grouping.
• How do you handle negatives in factorization?

  • Identify the signs of the factors.
  • Ensure the product is negative.
  • Adjust the signs accordingly.
• What is the significance of the a times c method in factorization?


  • It helps find suitable pairs of factors.
  • It ensures correct grouping for factorization.
• What is the first step in finding factors of 140?

  Write down the factors of 140
• Why is 140 not in the three times table?

  The digits do not add to a multiple of three
• What are the factors of 140 mentioned?

  1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140
• What is the result of 10 times 14?

  140
• Why are 10 and 14 both not in the four times table?

  Neither number is divisible by 4
• What does the expression $\frac{4m + 10 + m + 14}{4} =$$\frac{7}{2}$ represent?


  It represents a simplified equation
• How can you simplify $4m +$$10 +$$m +$$14$?


  Combine like terms to get $5m +$$24$
• What can be factored out of $4m +$$10$?


  2
• What is the result of multiplying the second bracket by 2?

  It gives $2m +$$5$
• What is the first step in solving $6x^2$?


  Factor it into $(6x)(x)$
• What is the product of $6$ and $-10$?


  -60
• Which pairs of factors multiply to give $-54$?


  3 and -18 or -6 and -9
• What is the result of $2B +$$3 =$$0$?


  B = $-3/2$
• What is the solution for $B$ when $B - 9 =$$0$?


  B = 9
• How do you solve $3x^2 - 19x +$$6 =$$0$?


  Factor it into $(3x - 1)(x - 6)$