Factorising

• What is factorisation?

  A factorised expression is one written as the product of two or more terms.
• How is the expression 3(x + 2) classified?

  It is classified as factorised because it is written as a product.

  
• Why is 3x + 6 not considered factorised?

  Because it is expressed as a sum of terms rather than a product.

  
• How can the number 12 be factorised?

  12 can be factorised as \(12 = 2 \times 2 \times 3\).

  
• What is the opposite of expanding brackets in algebra?

  Factorisation is the opposite of expanding brackets.
• How do you factorise the expression 12x + 18x?

  By finding the highest common factor, which is \(6x\), and rewriting it as \(6x(2x + 3)\).

  
• What is the highest common factor of 12 and 18?

  The highest common factor is 6.
• What is the factorised form of 12x + 18x?


  6x(2x + 3)

  
• How can you check if your factorisation is correct?

  By expanding the brackets in your answer to see if you get the original expression.
• What is the factorised form of 5x + 15?

  5(x + 3)

  
• What is the highest common factor of 5 and 15?

  The highest common factor is 5.
• How do you factorise the expression 30x - 24x?

  By finding the highest common factor, which is \(6x\), and rewriting it as \(6x(5 - 4)\).
• What is the factorised form of 30x - 24x?

  6x(5 - 4)

  
• How do you factorise expressions with common brackets?

  You take out the common bracket as a common factor.
• What is the factorised form of 3x(t + 4) + 2(t + 4)?

  (t + 4)(3x + 2)

  
• What is factorising by grouping?

  It involves grouping terms with common factors and factoring them out.
• How do you factorise the expression xy + px + qy + pq?


  By grouping to get (y + p)(x + q).

  
• What is the first step in factorising by grouping?

  Group the first pair of terms and factor out the common factor.
• What is a quadratic expression?

  A quadratic expression is in the form \(ax^2 + bx + c\) where \(a \neq 0\).

  
• What is a monic quadratic expression?

  A monic quadratic expression is when \(a = 1\).

  
• What is a non-monic quadratic expression?

  A non-monic quadratic expression is when \(a \neq 1\).
• How do you factorise the quadratic expression \(x^2 - 2x - 8\) by inspection?

  By finding numbers that multiply to -8 and add to -2, which are -4 and +2.
• What are the factors of the quadratic expression \(x^2 - 2x - 8\)?


  (x + 2)(x - 4)

  
• What is the first step in factorising \(x^2 - 2x - 8\) by grouping?

  Rewrite the middle term using the numbers that satisfy the conditions.
• How do you factorise \(x^2 - 5x + 6\) by splitting the middle term?

  By finding numbers that multiply to 6 and sum to -5, which are -3 and -2.

  
• What is the factorised form of \(x^2 - 5x + 6\)?


  (x - 2)(x - 3)

  
• What is the method used to factorise \(x^2 - 2x - 24\) using a grid?

  By finding numbers that multiply to -24 and sum to -2, which are +4 and -6.
• What is the factorised form of \(x^2 - 2x - 24\)?


  (x + 4)(x - 6)

  
• How do you factorise a harder quadratic expression like \(4x^2 - 25x - 21\)?

  By finding numbers that multiply to \(4 \times -21 = -84\) and add to -25.

  
• What is the first step in factorising \(4x^2 - 25x - 21\) by grouping?

  Rewrite the middle term using -28x and +3x.

  
• What do you do after rewriting the middle term in \(4x^2 - 25x - 21\)?

  Group and factorise the first two terms and the second two terms.
• What is the common factor in the expression \(4x^2 - 28x + 3x - 21\)?


  The common factor is \((x - 7)\).

  
• What is the final factorised form of \(4x^2 - 25x - 21\)?

  (x - 7)(4x + 3)

  
• What are the methods for factorising simple quadratics?

  1. Factorising by inspection
  2. Factorising by grouping
  3. Factorising by using a grid
• What should you do after factorising an expression?

  • Expand the expression to check your answer.
  • Ensure you get the same expression as the one you were trying to factorise.

  
• What are the steps for factorising by grouping?

  1. Group terms with common factors.
  2. Factor out the common factors from each group.
  3. Factor out the common bracket.
• What are the characteristics of a quadratic expression?


  • It is in the form \(ax^2 + bx + c\).
  • \(a \neq 0\).
  • If \(a = 1\), it is a monic quadratic.
  • If \(a \neq 1\), it is a non-monic quadratic.
• What are the conditions for factorising quadratics by inspection?

  • Find two numbers that multiply to \(c\).
  • Find two numbers that add to \(b\).
• What is the process for factorising quadratics using a grid?

  1. Identify two numbers that multiply to \(c\) and add to \(b\).
  2. Split the middle term and create a grid.
  3. Use the grid to find the factors.
• What is the process for factorising harder quadratics?


  1. Multiply \(a\) and \(c\).
  2. Find two numbers that multiply to \(ac\) and add to \(b\).
  3. Rewrite the middle term and group.
  4. Factor out the common factors.