The document provides examples of factorizing quadratic equations over 12 minutes with step-by-step instructions. It begins by defining factorizing as "putting in brackets" and provides rules for determining the signs in the factors based on the signs of the terms. Then, 8 practice problems are presented and the student is timed for 12 minutes to factorize the equations. After time expires, the answers are provided.

1. Multiplying out simple equations
1. 7x(2xy – 4x)
2. 15b(a – 3ab)
3. 9(ef + 3e)
4. 3ab(ab – 5b)
5. 5pq(3q – 2p + q²)
6. 3n(3mn – 4m + jm)
7. 2stu(5s – 3t² + 2su)
8. ab²(a³ – a + 2a²b)

2. Today I will factorise
quadratic equations.
Grade B

3. Things to remember
Example 5. 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