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Quadratic Factorisation Techniques
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Quadratic Factorisation Techniques
📚 Part 1: Daily Review & Prior Knowledge
1. Expand the following expression:
(x + 3)(x + 2) = _______________
2. Which of the following is the correct factorisation of x² + 7x + 12?
(x + 3)(x + 4)
(x + 2)(x + 6)
(x + 1)(x + 12)
(x + 7)(x + 12)
3. What are the factors of 15 that add to 8?
Factors: _____ and _____
✏️ Part 2: Symbolic Factorisation Methods
4. Factorise the following monic quadratics algebraically:
a) x² + 9x + 14 = _______________
b) x² + 6x + 8 = _______________
c) x² - 5x + 6 = _______________
5. Complete the square for x² + 8x + 7. Show your working:
6. Using the quadratic formula, solve x² + 4x - 5 = 0:
Quadratic Formula: x = (-b ± √(b² - 4ac)) / 2a
7. For the equation x² + 2x + 5 = 0, what does the discriminant tell us about the solutions?
Two real solutions
One repeated real solution
No real solutions
🎯 Part 3: Application & Extension
8. A quadratic function has roots at x = -2 and x = 3. Write the quadratic in factorised form:
y = _______________
9. Extension: The height of a ball thrown upward is given by h = -5t² + 20t + 25, where h is height in metres and t is time in seconds. When does the ball hit the ground? (Hint: h = 0)
10. Explain the connection between factorising a quadratic and finding where its graph crosses the x-axis:
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