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Brackets & Factors

Brackets & Factors. OCR Stage 6. What is 3(2 + 4) ?. 3 ‘lots’ of ‘2 + 4’. = 3 ‘lots’ of 6. = 18. 4. 2. x. = 18. 3. 12. 6. What is 3(x + 4) ?. 3 ‘lots’ of ‘x + 4’. 4. x. x. 3. 3x. 12. = 3x + 12. What is 5(2x + 1) ?. 5 ‘lots’ of ‘2x + 1’. 1. 2x. x. 5. 10x. 5. = 10x + 5.

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Brackets & Factors

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  1. Brackets & Factors OCR Stage 6

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

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

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

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

  6. What is x(x + 3) ? x ‘lots’ of ‘x + 3’ What is x times x? 3 x x = x2 + 3x x x2 3x

  7. What is 2x(x - 3) ? 2x ‘lots’ of ‘x - 3’ -3 x x 2x 2x2 -6x = 2x2 – 6x

  8. What is -x(2x + 3) ? -x ‘lots’ of ‘2x + 3’ 3 2x x -x -2x2 -3x = -2x2 – 3x We call this process ‘expanding a bracket’

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

  10. 4x + 2 Eg Factorise 4x + 2 What number divides into BOTH parts of the expression EXACTLY? 2x +1 2 = 2(2x + 1) How could we check this?

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

  12. Eg Factorise x2 + x What number divides into BOTH parts of the expression EXACTLY? x + 1 x x2 + x = x(x + 1)

  13. Eg Factorise 8x2 – 4x What number divides into BOTH parts of the expression EXACTLY? 2x - 1 4x 8x2 – 4x = 4x(2x - 1)

  14. Eg Factorise 6 - 4x2 What number divides into BOTH parts of the expression EXACTLY? 3 - 2x2 2 6 - 4x2 = 2(3 – 2x2)

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