Warm up Notes Preliminary Activity Activity For Fun

Factorising 1

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Review Questions

1. Write the conjugate for 3√5 + 6

2. Rationalise the denominator √5 + 2 √3

3. Simplify 8√2 √7

4. Find 1021/2% of $18.20

5. What percentage is $20.84 of $36?

6. Decrease $34.60 by 81/2%.

7. Write in scientific notationa) 0.000 000 064b) 1 600

8. Expand (3n - 1)(3n - 1)

3√5 - 6

√15 + 2√3 3

8√14 7

$18.66

57.9%

$31.66

6.4 x 10-8

1.6 x 103

9n2 - 6n + 1

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a(b + c) = ab + ac expanding the product

and ab + ac = a(b + c) factorising

These are opposite processes. It is often necessary to factorise expressions.To factorise an expression we follow these steps:

1. look for common factors in all terms

2. look for common factors in pairs of terms - grouping in pairs

3. look for the difference of two squares

4. look for quadratic trinomials.

Write an example for each of the four steps.

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Examples.

Factorise the following expressions

1. 2x2 + 6x

2. am - an + bn - bm

3. 9y2 - 16

4. x2 - 3x - 10

5. 2x2 - 5x - 12

2x(x + 3)

a(m - n) - b(m - n) note: make b negative so that the terms in each bracket are the same(a - b)(m - n)

(3y - 4)(3y + 4)

(x - 5)(x + 2)

(2x - 8)(2x + 3) 2(x - 4)(2x + 3)

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41.7%

56.3%

75.7%

page 38 Exercise 3.1 Q 1,13, 31, 32, 33, 34, 35, 36

page 39 Exercise 3.2 Q 1, 2, 3, 17, 18, 19, 20

page 39 Exercise 3.3 Q 1, 4, 7, 25, 26, 27, 28, 29, 30

page 40 Exercise 3.4 Q 2, 3, 4, 34, 35, 36, 37

page 41 Exercise 3.5 Q 1, 2, 3, 4, 5, 41, 42, 43, 44, 45

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$1 104

$1 096.50

$211.70

50.9%

$17.25

8.5%

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