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Published byJessie Mills Modified over 9 years ago
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Starter Revision Worksheet
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Factorising is the opposite of expanding – putting brackets back into the expression Note 7: Factorising Brackets
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Common Factor Look for the highest common factor in the numbers and the lowest power for each common letter Place them outside the brackets
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+ () This needs to be a common factor that appears in both terms. Choose 3 3 Now think..... 3 ? gives 3a a Now think..... 3 ? gives 6 2 3a + 6 = Answer: 3a + 6 = 3(a + 2) Finally…..Check by expanding 3(a + 2) to make sure it is equal to 3a + 6.
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Example 2 Factorise 3c + c 2 3c + c 2 = + () This needs to be a common factor that appears in both terms. Pick the BIGGEST! c Now think..... c ? gives 3c 3 Now think..... c ? gives c 2 c
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Example 3 Factorise 12ab 2 – 9a 2 bc 12ab 2 – 9a 2 bc = – () This needs to be a common factor that appears in both terms. Pick the BIGGEST! 3ab Now think..... 3ab ? gives 12ab 2 4b4b Now think..... 3ab ? Gives 9a 2 bc 3ac
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To factorise an equation in the form x 2 + bx + c List the factor pairs of c Look for the pair that add to b Place in brackets (x ___) (x ___) Quadratics
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Factorise x 2 + 11x + 24 Examples: 124 212 38 46 = (x + 3)(x + 8) Factorise x 2 + x - 12 1-12 2-6 3-4 -112 -26 -34 = (x - 3)(x + 4)
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If there is NO middle term – it is the difference between two squares. Example: Factorise x 2 – 64 = 16 – 4a 2 = 25x 2 – 36y 2 = (x – 8)(x + 8) (5x – 6y)(5x + 6y) (4 – 2a)(4 + 2a)
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Some quadratic expressions have a common factor and the two factors in brackets. Example: Factorise 3x 2 – 3x - 18 = 3(x 2 - x - 6) 3(x – 3)(x + 2)
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Page 47 Exercise I and J
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