Factoring into one bracket

• What does it mean to factorize an expression?

  It means to express it as a product of its factors.
• What is the HCF of 4 and 12?

  4
• What is the highest common factor (HCF)?

  The HCF is the largest number that divides two or more numbers exactly.
• How do you determine the HCF of two numbers?

  You find the largest number that divides both numbers without leaving a remainder.
• What do you multiply 4 by to get back to 4x?


  X
• What do you multiply 4 by to get back to 12?

  3
• How can you check if your factorization is correct?

  You can multiply the factors back together to see if you get the original expression.
• What is the HCF of 6 and 9?

  3
• What do you multiply 3 by to get back to 9y?

  3y
• What do you multiply 3 by to get back to 6?

  2
• What is the HCF of 18 and 21?

  3
• What do you multiply 3y by to get back to 18xy?

  6x
• What do you multiply 3y by to get back to 21y?

  7
• What is the HCF of 24 and 32?

  8
• What do you multiply 8x by to get back to 32x?

  • 4
• What do you multiply 8x by to get back to 24x²?

  3x
• What do you multiply 3 by to get back to 6xy?

  2xy
• What is the HCF of 6, 9, and 12?

  3
• What do you multiply 3 by to get back to 9y?

  3
• What do you multiply 3 by to get back to 12?

  4
• What are the steps to factorize an expression using the highest common factor?

  1. Identify the highest common factor of the terms.
  2. Write down the HCF outside the brackets.
  3. Determine what to multiply the HCF by to get each term back.
  4. Write the results inside the brackets.
• How does the process of factorization help in simplifying expressions?

  • It reduces the complexity of expressions.
  • It allows for easier manipulation in equations.
  • It helps in solving polynomial equations more efficiently.
• What are the common mistakes to avoid when factorizing?

  • Forgetting to include all common factors.
  • Not checking the factorization by multiplying back.
  • Confusing addition and multiplication in the process.