Year 10 - Maths
Factorising quadratics of the form ax^2 + bx + c
Algebraic manipulation
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In algebraic manipulation, pupils use apply knowledge of the distributive law to find the product of two binomaials in order to factorise quadratics.
Lesson Summary
You will learn to factorise quadratics of the form ax^2 + bx + c.
Key Notes
- For these cases, there are restrictions on how you decompose the x term.
- Using the area model can show why this is.
- By considering the structure, you can deduce how to decompose the x term.
Vocabulary To Learn
- Factorise: To factorise is to express a term as the product of its factors.
- Quadratic: A quadratic is an equation, graph, or sequence whereby the highest exponent of the variable is 2
Common Mistakes To Avoid
- Believing the constants in the binomials must sum to the coefficient of x and multiply to the constant in the quadratic.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
For these cases, there are restrictions on how you decompose the x term. Using the area model can show why this is.
2. Use this key word in a maths sentence and explain it clearly. 'Factorise'
To factorise is to express a term as the product of its factors. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Believing the constants in the binomials must sum to the coefficient of x and multiply to the constant in the quadratic. Correction: Use an area model to show what is happening when the coefficient of x^2 is not 1. Pupils should always check their answers by expanding.
More Lessons In This Unit
- Advanced problem solving with algebraic manipulation Study Guide
- Checking and securing understanding of changing the subject Study Guide
- Checking and securing understanding of expanding a single bracket Study Guide
- Checking and securing understanding of factorising Study Guide
- Checking and securing understanding of forming linear equations Study Guide
- Checking and securing understanding of simplifying Study Guide
- Checking and securing understanding of solving and interpreting linear equations Study Guide
- Checking and securing understanding of substitution Study Guide
- Checking and securing understanding of the product of two binomials Study Guide
- Factorising a quadratic expression Study Guide
- Factorising using the difference of two squares Study Guide
- Further algebraic terminology Study Guide
- Problem solving with algebraic manipulation Study Guide
- Solving complex quadratic equations by completing the square Study Guide
- Solving quadratic equations by completing the square Study Guide
- Solving quadratic equations by factorising Study Guide
- Solving quadratic equations by factorising where rearrangement is required Study Guide
- Solving quadratic equations by using the formula Study Guide
- The product of three binomials Study Guide
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