Contenu connexe Similaire à Factorise quadratic equations (20) Plus de Angela Phillips (20) Factorise quadratic equations2. 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
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