Factors A factor is a number or letter that will divide exactly into another number or expression without leaving a remainder Examples (a) Factors of 12…

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Presentation transcript:

Factors A factor is a number or letter that will divide exactly into another number or expression without leaving a remainder Examples (a) Factors of 12… (b) Factors of 3x2 12 12 12 3x2 3x2 3x2 1 12 2 6 3 4 1 3x2 3 x2 x 3x 1, 2, 3, 4, 6, 12 1, 3, x, 3x, x2, 3x2

Factors (c) Factors of 18 (d) Factors of 6x2 1 2 3 6 1 2 3 9 18 6x2 3x2 2x2 x2 x 2x 3x 6x (e) Factors of 9x 1 3 9 x 3x 9x

Highest Common Factors 1 2 3 4 6 12 1 2 4 8 16 1 5 a 5a 1 a a2 1 2 4 8 x 2x 4x 8x 4x2 8x 1 2 x 2x 4x x2 2x2 4x2 12 16 5a a2 The highest common factor (HCF) is the largest factor that appears in both lists.

Putting The Brackets Back In It is not only important to be able to multiply out brackets but also to be able to put the brackets back. This process is called FACTORISATION. Consider the expression below : Can you find a Highest Common Factor (HCF)? 6a + 12 = 6 ( a + 2 ) 6 is the common factor Now take 6 outside the bracket and work out what goes inside the bracket.

Now factorise the following expressions: 5 ( x + 2 ) (2) 7x + 21 = 7 ( x + 3 ) (3) 6x - 9 = 3 ( 2x - 3 ) (4) 15x - 20 = 5 ( 3x - 4 ) (5) 24x + 8 = 8 ( 3x + 1 )

(6) 6x + 12 = 6 ( x + 2 ) (7) 9x - 18 = 9 ( x - 2 ) (8) 8x + 12 = 4 ( 2x + 3 ) (9) 7x - 21 = 7 ( x - 3 ) (10) 10x + 15 = 5 ( 2x + 3 )

Multiplying Out Brackets Reminder (1) 3t( 2t + 5 ) = 6t2 + 15t So 6t2 + 15t factorised = 3t(2t + 5) (2) 4w ( 3w - 7 ) = 12w2 - 28w So 12w2 – 28w factorised = 4w(3w - 7) (3) 5a ( 2a + 9 ) = 10a2 + 45a So 10a2 + 45a factorised = 5a(2a + 9) (4) 2z ( 5z - 8 ) = 10z2 - 16z So 10z2 – 16z factorised = 2z(5z - 8)

Factorise the following expressions: (1) 5wg – 10wm (3) 9ab + 12bc = 5w ( g + 2m ) = 3b ( 3a - 4c ) (2) 16xy – 8xw (4) 6x2 + 9 xy = 8x ( 2y - w ) = 3x ( 2x + 3y )

Set 1: Factorise each of the following Question Factorize 1 8x - 32 2 12y + 30 3 5x - 50 4 7m - 7 5 6t - 4 6 8 – 4n 7 15f - 30 8 12c + 16 9 2x2 + 4x 10 5y2 – 20y 8(x – 4) 6(y + 5) 5(x + 5) 7(m - 1) 2(3t - 2) 4(2 - n) 5(3f - 6) 4(3c + 4) 2x(x + 2) 5y(y - 4)

Question Factorize 11 a2 + a 12 15m + 30m2 13 2x – 2x2 14 3t + 27t2 15 ab + 5b 16 pq – q2 17 x – 4x2 18 9y3 – 18y2 19 16x2 – 8x3 20 5x – 5x2 a(a + 1) 5m(3 + 6m) 2x(1 - x) 3t(1 + 9t) b(a + 5) q(p - q) x(1 – 4x) 9y2(y – 2) 8x2(2 – x) 5x(1 – x)

Set 2: Factorise each of the following Question Factorize 1 5x - 20 2 9y + 81 3 2x + 2 4 6k - 60 5 16y - 24 6 18 + 6m 7 25f - 35 8 4c + 6 9 5x2 + 5x 10 6y2 – 24y 5(x - 4) 9(y + 9) 2(x + 1) 6(k - 10) 8(2y - 3) 6(3 + 2m) 5(5f - 7) 2(2c + 3) 5x(x + 1) 6y(y - 4)

Question Factorize 11 2a2 + 4a 12 12m + 32m2 13 12x – 4x2 14 7t + 56t2 15 8b - 48b2 16 2pq – 4q2 17 4x – 4x2 18 8c3 + 20c2 19 4x2 + 32x3 20 x – 12x2 2a(a + 2) 4m(3 + 8m) 4x(3 - x) 7t(1 + 8t) 8b(1 - 6b) 2q(p – 2q) 4x(1 – x) 4c2(2c + 5) 4x2(1 + 8x) x(1 - 12x)

Factorise the following More Practice Factorise the following 9p – 63 8x + 20 35p – 28 56y – 32 36t + 45v 33a – 18b 84c + 56d 81 – 54k 9. 24ab + 18a 10. 21x – 6xy 11. 4t2 + 8t 12. 8y2 - 32y 13. 10b2 + 15b 14. 12k + 2k2 15. 6c2 + 9cd 16. 7v2 + 91v 17. 6ab – 3a2b 18. 4x2y + 8xy 19. 5p2q – 5pq2 20. 2c2d + 6cd2 21. a3b + ab3 22. 8x3 + 12xy 23. 9g2h – 18gh3 24. 48t2v2 – 8t2