The document provides instructions and examples for students to practice factorizing quadratic equations within timed intervals. It begins by defining factorizing as "putting in brackets" and provides the key rules and patterns for factorizing different types of quadratic expressions. Then, 8 practice problems are presented with decreasing time limits. Finally, the factored solutions are provided along with 2 additional problems to check understanding.

1. Entry Activity – Copy and complete

2. Friday 22nd February 2008
Today I will factorise
quadratic equations.
Grade B

3. Things to remember
Example 1. Factorise Factorise means put in
a² - 8a + 16 brackets.
• x²+ ax + b = (x + ?)(x + ?)
Since everything is
positive.
• x² – ax + b = (x – ?)(x – ?)
Since –ve × –ve = +ve.
• x²+ ax – b = (x + ?)(x – ?)
Since +ve × –ve = –ve.
• x²– ax – b = (x + ?)(x – ?)

4. You have 12
minutes Factorise equations
1. a² + 5a + 6 Factorise means put in
2. b² + 7b +12 brackets.
• x²+ ax + b = (x + ?)(x + ?)
3. c² - 6c + 9 Since everything is
4. d² + d – 20 positive.
• x² – ax + b = (x – ?)(x – ?)
5. e² - 12e + 35 Since –ve × –ve = +ve.
6. f² +2f – 8 • x²+ ax – b = (x + ?)(x – ?)
Since +ve × –ve = –ve.
7. g² +2g – 24
• x²– ax – b = (x + ?)(x – ?)
8. h² - 11h + 30

5. You have 11
minutes Factorise equations
1. a² + 5a + 6 Factorise means put in
2. b² + 7b +12 brackets.
• x²+ ax + b = (x + ?)(x + ?)
3. c² - 6c + 9 Since everything is
4. d² + d – 20 positive.
• x² – ax + b = (x – ?)(x – ?)
5. e² - 12e + 35 Since –ve × –ve = +ve.
6. f² +2f – 8 • x²+ ax – b = (x + ?)(x – ?)
Since +ve × –ve = –ve.
7. g² +2g – 24
• x²– ax – b = (x + ?)(x – ?)
8. h² - 11h + 30

6. You have 10
minutes Factorise equations
1. a² + 5a + 6 Factorise means put in
2. b² + 7b +12 brackets.
• x²+ ax + b = (x + ?)(x + ?)
3. c² - 6c + 9 Since everything is
4. d² + d – 20 positive.
• x² – ax + b = (x – ?)(x – ?)
5. e² - 12e + 35 Since –ve × –ve = +ve.
6. f² +2f – 8 • x²+ ax – b = (x + ?)(x – ?)
Since +ve × –ve = –ve.
7. g² +2g – 24
• x²– ax – b = (x + ?)(x – ?)
8. h² - 11h + 30

7. You have 9
minutes Factorise equations
1. a² + 5a + 6 Factorise means put in
2. b² + 7b +12 brackets.
• x²+ ax + b = (x + ?)(x + ?)
3. c² - 6c + 9 Since everything is
4. d² + d – 20 positive.
• x² – ax + b = (x – ?)(x – ?)
5. e² - 12e + 35 Since –ve × –ve = +ve.
6. f² +2f – 8 • x²+ ax – b = (x + ?)(x – ?)
Since +ve × –ve = –ve.
7. g² +2g – 24
• x²– ax – b = (x + ?)(x – ?)
8. h² - 11h + 30

8. You have 8
minutes Factorise equations
1. a² + 5a + 6 Factorise means put in
2. b² + 7b +12 brackets.
• x²+ ax + b = (x + ?)(x + ?)
3. c² - 6c + 9 Since everything is
4. d² + d – 20 positive.
• x² – ax + b = (x – ?)(x – ?)
5. e² - 12e + 35 Since –ve × –ve = +ve.
6. f² +2f – 8 • x²+ ax – b = (x + ?)(x – ?)
Since +ve × –ve = –ve.
7. g² +2g – 24
• x²– ax – b = (x + ?)(x – ?)
8. h² - 11h + 30

9. You have 7
minutes Factorise equations
1. a² + 5a + 6 Factorise means put in
2. b² + 7b +12 brackets.
• x²+ ax + b = (x + ?)(x + ?)
3. c² - 6c + 9 Since everything is
4. d² + d – 20 positive.
• x² – ax + b = (x – ?)(x – ?)
5. e² - 12e + 35 Since –ve × –ve = +ve.
6. f² +2f – 8 • x²+ ax – b = (x + ?)(x – ?)
Since +ve × –ve = –ve.
7. g² +2g – 24
• x²– ax – b = (x + ?)(x – ?)
8. h² - 11h + 30

10. You have 6
minutes Factorise equations
1. a² + 5a + 6 Factorise means put in
2. b² + 7b +12 brackets.
• x²+ ax + b = (x + ?)(x + ?)
3. c² - 6c + 9 Since everything is
4. d² + d – 20 positive.
• x² – ax + b = (x – ?)(x – ?)
5. e² - 12e + 35 Since –ve × –ve = +ve.
6. f² +2f – 8 • x²+ ax – b = (x + ?)(x – ?)
Since +ve × –ve = –ve.
7. g² +2g – 24
• x²– ax – b = (x + ?)(x – ?)
8. h² - 11h + 30

11. You have 5
minutes Factorise equations
1. a² + 5a + 6 Factorise means put in
2. b² + 7b +12 brackets.
• x²+ ax + b = (x + ?)(x + ?)
3. c² - 6c + 9 Since everything is
4. d² + d – 20 positive.
• x² – ax + b = (x – ?)(x – ?)
5. e² - 12e + 35 Since –ve × –ve = +ve.
6. f² +2f – 8 • x²+ ax – b = (x + ?)(x – ?)
Since +ve × –ve = –ve.
7. g² +2g – 24
• x²– ax – b = (x + ?)(x – ?)
8. h² - 11h + 30

12. You have 4
minutes Factorise equations
1. a² + 5a + 6 Factorise means put in
2. b² + 7b +12 brackets.
• x²+ ax + b = (x + ?)(x + ?)
3. c² - 6c + 9 Since everything is
4. d² + d – 20 positive.
• x² – ax + b = (x – ?)(x – ?)
5. e² - 12e + 35 Since –ve × –ve = +ve.
6. f² +2f – 8 • x²+ ax – b = (x + ?)(x – ?)
Since +ve × –ve = –ve.
7. g² +2g – 24
• x²– ax – b = (x + ?)(x – ?)
8. h² - 11h + 30

13. You have 3
minutes Factorise equations
1. a² + 5a + 6 Factorise means put in
2. b² + 7b +12 brackets.
• x²+ ax + b = (x + ?)(x + ?)
3. c² - 6c + 9 Since everything is
4. d² + d – 20 positive.
• x² – ax + b = (x – ?)(x – ?)
5. e² - 12e + 35 Since –ve × –ve = +ve.
6. f² +2f – 8 • x²+ ax – b = (x + ?)(x – ?)
Since +ve × –ve = –ve.
7. g² +2g – 24
• x²– ax – b = (x + ?)(x – ?)
8. h² - 11h + 30

14. You have 2
minutes Factorise equations
1. a² + 5a + 6 Factorise means put in
2. b² + 7b +12 brackets.
• x²+ ax + b = (x + ?)(x + ?)
3. c² - 6c + 9 Since everything is
4. d² + d – 20 positive.
• x² – ax + b = (x – ?)(x – ?)
5. e² - 12e + 35 Since –ve × –ve = +ve.
6. f² +2f – 8 • x²+ ax – b = (x + ?)(x – ?)
Since +ve × –ve = –ve.
7. g² +2g – 24
• x²– ax – b = (x + ?)(x – ?)
8. h² - 11h + 30

15. You have 1
minutes Factorise equations
1. a² + 5a + 6 Factorise means put in
2. b² + 7b +12 brackets.
• x²+ ax + b = (x + ?)(x + ?)
3. c² - 6c + 9 Since everything is
4. d² + d – 20 positive.
• x² – ax + b = (x – ?)(x – ?)
5. e² - 12e + 35 Since –ve × –ve = +ve.
6. f² +2f – 8 • x²+ ax – b = (x + ?)(x – ?)
Since +ve × –ve = –ve.
7. g² +2g – 24
• x²– ax – b = (x + ?)(x – ?)
8. h² - 11h + 30

16. Work for today

17. Answers

18. Answers
1. a² + 5a + 6 = (a + 2)(a + 3)
2. b² + 7b +12 = (b + 4)(b + 3)
3. c² - 6c + 9 = (c – 3)(c – 3)
4. d² + d – 20 = (d – 4)(d + 5)
5. e² - 12e + 35 = (e – 5)(e – 7)
6. f² +2f – 8 = (f – 2)(f + 4)
7. g² +2g – 24 = (g + 6)(g – 4)
8. h² - 11h + 30 = (h – 5)(h – 6)

19. Plenary
• Today’s learning objective was ‘Today I will
factorise quadratic equations’ complete the
questions below to prove you have met the
objective!
Multiply out
a) 5xy(2x – 4) b) (x – 4)(x + 2)
Factorise
c) 4x² - 12xy d) x² - 3x - 10