Questions and Answers
What is the complete factorisation of 5k + 25h - 15?
5(k + 5h - 3)
What is the complete factorisation of x² - 6x?
x(x - 6)
What is the complete factorisation of 9x² + 12xy?
3x(3x + 4y)
What is the complete factorisation of 14ab² - 35a²b + 7ab?
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What are the factors of x² + 12x + 35?
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What are the factors of a² + 5a - 24?
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What is the factorisation of h² - 36?
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What are the factors of y² - 6y + 8?
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What is the factorisation of 3x² - x - 4?
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What is the factorisation of 2w² - 11w + 15?
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What should you do when asked to factorise a short expression?
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What is expected when asked to factorise 'fully' or 'completely'?
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What happens when you factorise a quadratic expression?
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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).
- Use separation method:
-
2w² - 11w + 15:
- Apply separation method:
- Multiply 2 by 15 to get 30.
- Pairs of -30 summing to -11 give: (w - 3)(2w - 5).
- Apply separation method:
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.
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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.