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Brackets & Factors OCR Stage 6

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What is 3(2 + 4) ? 3 ‘lots’ of ‘2 + 4’= 3 ‘lots’ of 6= 18 2 4 3 x 6 12 = 18

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What is 3(x + 4) ? x 4 3 x 3x12 = 3x + 12 3 ‘lots’ of ‘x + 4’

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What is 5(2x + 1) ? 2x 1 5 x 10x5 = 10x + 5 5 ‘lots’ of ‘2x + 1’

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What is 4(x - 2) ? x -2 4 x 4x-8 = 4x - 8 4 ‘lots’ of ‘x - 2’

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What is x(x + 3) ? x 3 x x x2x2 3x = x 2 + 3x x ‘lots’ of ‘x + 3’ What is x times x?

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What is 2x(x - 3) ? x -3 2x x 2x 2 -6x = 2x 2 – 6x 2x ‘lots’ of ‘x - 3’

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What is -x(2x + 3) ? 2x 3 -x x -2x 2 -3x = -2x 2 – 3x -x ‘lots’ of ‘2x + 3’ We call this process ‘expanding a bracket’

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Factorising an expression This is the reverse of expanding a bracket Eg Factorise 4x + 2 What is a Factor? A FACTOR of a number is a number that divides into the number EXACTLY

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Eg Factorise 4x + 2 What number divides into BOTH parts of the expression EXACTLY? 2 4x + 2 2x+1 = 2(2x + 1) How could we check this?

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Eg Factorise 6x - 9 What number divides into BOTH parts of the expression EXACTLY? 36x - 9 2x- 3 = 3(2x – 3)

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Eg Factorise x 2 + x What number divides into BOTH parts of the expression EXACTLY? xx 2 + x x+ 1 = x(x + 1)

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Eg Factorise 8x 2 – 4x What number divides into BOTH parts of the expression EXACTLY? 4x8x 2 – 4x 2x- 1 = 4x(2x - 1)

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Eg Factorise 6 - 4x 2 What number divides into BOTH parts of the expression EXACTLY? 26 - 4x 2 3- 2x 2 = 2(3 – 2x 2 )

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AS Mathematics Algebra – Quadratic equations. Objectives Be confident in the use of brackets Be able to factorise quadratic expressions Be able to solve.

AS Mathematics Algebra – Quadratic equations. Objectives Be confident in the use of brackets Be able to factorise quadratic expressions Be able to solve.

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