Factorising Algebraic Expressions

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.