Factorising Algebraic Expressions

Study Notes

Factorising Algebraic Expressions

Factorising involves identifying common factors in algebraic terms, allowing simplification and rewriting of expressions.

Simple Factorisation Examples

5k + 25h - 15: Common factor is 5.
- This simplifies to: 5(k + 5h - 3).
x² - 6x: Common factor is x.
- Resulting in: x(x - 6).
9x² + 12xy: Common factors are 3 and x.
- Simplification yields: 3x(3x + 4y).
14ab² - 35a²b + 7ab: Common factors are 7, a, and b.
- This results in: 7ab(2b - 5a + 1).

Quadratic Factorisation

x² + 12x + 35:
- Use double brackets; pairs of factors of 35 that add to 12 lead to: (x + 5)(x + 7).
a² + 5a - 24:
- Look for factors of -24 that sum to 5, resulting in: (a + 8)(a - 3).
h² - 36: Recognises it as a difference of squares.
- Factorised outcome: (h + 6)(h - 6).
y² - 6y + 8: Search for negative pairs that sum to -6.
- Factorisation gives: (y - 4)(y - 2).

Factorisation with Coefficients

3x² - x - 4:
- Use separation method:
  - Multiply 3 (coefficient of x²) by -4 (constant) to get -12.
  - Find pairs of -12 summing to -1, yielding: (3x - 4)(x + 1).
2w² - 11w + 15:
- Apply separation method:
  - Multiply 2 by 15 to get 30.
  - Pairs of -30 summing to -11 give: (w - 3)(2w - 5).

Guidelines for Factorisation

For short expressions, factor out a single factor in front of one bracket.
- Example: 6n - 9 = 3(2n - 3).
When asked to factorise "fully" or "completely", find multiple factors for a single bracket.
- Example: 4h³ + 8h = 4h(h² + 2).
Quadratics require formation of double brackets.
- General approach leads to results worth multiple marks.

Description

This quiz explores the process of factorising various algebraic expressions, focusing on identifying common factors for simplification. Participants will practice both simple factorisation and quadratic factorisation techniques, including examples with coefficients and differences of squares.