Chapter 1

1 Chapter 1. Exercise 1. (i) coefficient of x2 3. (ii) coefficient of x 9. (iii) independent term 5. 2. (i) degree 2. (ii) degree 3. (iii) degree 4. 4 4x 1, 1 is not a positive power;. 3. ___. x _3 3. x 2 , __ is not an integer. 2. 4. (i) 3x2 6x 7 5x2 2x 9 8x2 4x 2. (ii) x3 4x2 5x 3x3 6x2 x 4x3 2x2 6x (iii) x(x 4) 3x(2x 3) x2 4x 6x2 9x 7x2 5x (iv) 3(x2 7) 2x(3x 1) 7x 2 3x2 21 6x2 2x 7x 2. 9x2 9x 19. 5. (i) 3x2(4x 2) 5x2(2x 5) 12x3 6x2 10x3 25x2. 22x3 19x2. (ii) x3(x 2) 4x3(2x 6) x4 2x3 8x4 24x3. 9x4 26x3. (iii) x(x3 4x2 7x) 3x2(2x2 3x 4) x4 4x3 7x2 6x4 9x3 12x2. 7x4 5x3 5x2. (iv) 3x(x 7x 1) 2x (6x 5) 3x 21x2 3x 12x3 10x2.

2 2 2 3. 15x3 31x2 3x 6. (i) (x 4)(2x 5) 2x2 5x 8x 20 2x2 13x 20. (ii) (2x 3)(x 2) 2x2 4x 3x 6 2x2 x 6. (iii) (3x 2)(x 3) 3x2 9x 2x 6 3x2 7x 6. (iv) (3x 2)(4x 1) 12x2 3x 8x 2 12x2 11x 2. (v) (3x 1)(2x 5) 6x2 15x 2x 5 6x2 13x 5. (vi) (4x 1)(2x 6) 8x2 24x 2x 6 8x2 22x 6. (vii) (x 2)(x 2) x2 2x 2x 4 x2 4. (viii) (2x 5)(2x 5) 4x2 10x 10x 25 4x2 25. (ix) (ax by)(ax by) a2x2 abxy abxy b2y2 a2x2 b2y2. 7. (i) (x 2)2 x2 4x 4. (ii) (x 3)2 x2 6x 9. (iii) (x 5)2 x2 10x 25. (iv) (a b)2 a2 2ab b2. (v) (x y)2 x2 2xy y2. (vi) (a 2b)2 a2 4ab 4b2. (vii) (3x y)2 9x2 6xy y2. (viii) (x 5y)2 x2 10xy 25y2. (ix) (2x 3y)2 4x2 12xy 9y2. 1. Text & Tests 4 Solution 2.

3 Chapter 1. 1 2 x2 2(x) __ 1 2 x2 x __. (. 8. (i) x __. 2 ) () (). 1 __. 2 2. 1. 4. 2. 1. ( 1. ) ( ( ) ( )) (. 1. (ii) 8 x __ 8 x2 2(x) __ + ___ 2 8 x2 __. 4 4 4 2 16. 1. x + ___. ). 1. 8x2 4x + __. 2. (iii) (1 x) (1 2x x ) 1 2x x 2 2 2. 9. (i) x2 5x 25; No, cannot be written in the form (x k)2. (ii) 9x2 6x 1; No, cannot be written in the form (x k)2. (iii) 4 12x 9x2 (2 3x)2; YES. 10. px2 4x 1 (ax 1)2. px2 4x 1 can be written in the form (ax 1)2 a2x2 2ax 1. 2a 4 a 2. (ax 1)2 (2x 1)2 4x2 4x 1. p 4. 11. 25x2 tx 4 (5x 2)2 or 25x2 tx 4 (5x 2)2. 25x2 20x 4 25x2 20x 4. t 20 t 20. 12. 9x2 24x s (3x a)2 9x2 6ax a2. 6a 24. a 4. 9x2 24x s (3x 4)2.

4 9x2 24x 16. s 16. 13. (i) (x 2)(x2 2x 6) x3 2x2 6x 2x2 4x 12. x3 4x2 10x 12. (ii) (x 4)(2x2 3x 1) 2x3 3x2 x 8x2 12x 4. 2x3 5x2 13x 4. (iii) (2x 3)(x2 3x 2) 2x3 6x2 4x 3x2 9x 6. 2x3 3x2 5x 6. (iv) (3x 2)(2x 4x 2) 6x3 12x2 6x 4x2 8x 4. 2. 6x3 16x2 14x 4. 14. (x y)(x2 xy y2) x3 x2 y xy2 x2 y xy2 y3. x3 y3. 15. (x y)(x2 xy y2) x3 x2 y xy2 x2 y xy2 y3. x3 y3. 16. (2x 3)(3x2 2x 4) 6x3 4x2 8x 9x2 6x 12. 6x3 13x2 14x 12. coefficient of x 14. 17. (x 3)(x 4)(2x 1) (x 3)(2x2 x 8x 4). (x 3)(2x2 7x 4). 2x3 7x2 4x 6x2 21x 12. 2x3 x2 25x 12. 18. (x2 3x 2)(2x2 4x 1) 2x4 4x3 x2 6x3 12x2 3x 4x2 8x 2. 2x4 10x3 9x2 5x 2. 3. Text & Tests 4 Solution 19.

5 (3x2 5x 1)(2x2 6x 5); x2 coefficients include 15x2 30x2 2x2. 47x2. coefficient of x2 47. 3x 6 x 2. 20. (i) _____. 3. (ii) x 2.. _____ 2x x 2. x 3 3x2(x 2). 6x2 _____. (iii) 3x _____ x(x 2) x2 2x 3x 3x 15x2y 10xy2. (iv) _____ = 3x 2y 5xy 6x y 9xy2 3xy 2. 21. (i) _____ x 3y 1. 3xy 4 3x2(x2 3x 4). 9x3 12x2 _____. (ii) 6x _____. 2. 3x 3x2. x2 3x 4. 4. 12a2 b 4a 22. (i) _____. 3ab 4. 2. 12a bc 4ab (ii) _____. 3ac 2. 4xy2z (iii) _____ 2yz 2xy 3xy 12xy __y 4 ____. (iv) ____ ___. 2 . 2 6x 12x2 x (2x 1) (x 3). 2x2 5x 3 _____. 23. (i) _____ x 3. 2x 1 2x 1. 2. 2x 12 _____ 2(x 3) (x 2). 2(x2 x 6) _____. (ii) 2x _____ . x 3 x 3 x 3.

6 2(x 2) 2x 4. 2. 8x 6 2(4x 2. 2 (2x 1) (2x 3). 4x 3) _____. (iii) 8x _____ _____ . 4x 2 2(2x 1) 2 (2x 1). 2x 3. 24. (i) x2 7x 12. x 1 x3 8x2 19x 12. x3 x2. _____. 7x2 19x 12. 7x 2. 7x _____. 12x 12. 12x 12. _____. (ii) x2 1. 2x 1 2x3 x2 2x 1. 2x3 x2. _____. 2x 1. 2x 1. _____. (iii) x2 1. 3x 4 3x3 4x2 3x 4. 3x3. 4x2. _____. 3x 4. 3x 4. _____. 4. Chapter 1. (iv) 4x2 5x 6. x 3 4x3 7x2 21x 18. 4x 3. 12x2. _____. 5x2 21x 18. 5x2 15x _____. 6x 18. 6x 18. _____. (v) x2 5x 3. x 5 x3 22x 15. 3. 5x x_____2. 5x2 22x 15. 5x 2. 25x _____. 3x 15. 3x 15. _____. (vi) 2x2 3x 6. x 2 2x3 x2 12. 2x 3. 4x _____ 2. 3x2 12. 3x2. 6x _____. 6x 12.

7 6x 12. 25. (i) x 2. x 2 x3 2x2 2x 4. 2. x3 2x 2x2 4. 2x2. 4. (ii) x 3. x2 6x 9 x3 9x2 27x 27. 3. 6x2 9x x_____. 3x2 18x 27. 3x 2. 18x 27. _____. (iii) 3x 1. x2 x 2 3x3 2x2 7x 2. 3x 3. 3x2 6x _____. x2 x 2. x2 x 2. _____. (iv) x 2. 5x2 4x 1 5x3 14x2 7x 2. 5x3 4x2 x _____. 10x2 8x 2. 10x 2. 8x 2. _____. 26. (i) x2 2x 4. x 2 x3 8. 3. 2x2. x_____. 2x2 8. 2x 2. 4x _____. 4x 8. 4x 8. 5. Text & Tests 4 Solution (ii) 4x2 6xy 9y2. 2x 3y 8x3 27y3. 8x3 12x2y 12x2y 27y3. 12x 2. y 18xy2. _____. 18xy2 27y3. 18xy2 27y3. Exercise 1. x cm length of smaller side, (x 4) cm length of longer side. (i) A(x) x(x 4) (x2 4x) cm2. (ii) P(x) 2[x (x 4)] (4x 8) cm 2.

8 (i) Area length width 6x2 4x 2. Area _____. width _____. length 3x 1. (3x 1)(2x 2). _____. 2x 2. 3x 1. (ii) Perimeter 2(length width). 2((3x 1) (2x 2)). P(x) 10x 2. 3. (a) V(x) (2x 3)(x)(x 1). (2x 3)(x2 x). 2x3 2x2 3x2 3x 2x3 5x2 3x (b) S(x) (x)(2x 3) 2(x)(x 1) 2(2x 3)(x 1). 2x2 3x 2x2 2x 4x2 4x 6x 6. 8x2 15x 6. (c) (i) V(5) 2(5)3 5(5)2 3(5) 390 cm3. (ii) S(5) 8(5)2 15(5) 6 281 cm2. 4. f (x) 2x3 x2 5x 4. (a) f (0) 2(0)3 (0)2 5(0) 4 4. (b) f (1) 2(1)3 (1)2 5(1) 4 8. (c) f ( 2) 2( 2)3 ( 2)2 5( 2) 4 14. (d) f (3a) 2(3a)3 (3a)2 5(3a) 4 54a3 9a2 15a 4. 5. f (x) x2 3x 6. (a) f (0) (0)2 3(0) 6 6. (b) f ( 5) ( 5)2 3( 5) 6 46. 1 2 3 __.

9 ( ) ( ) ( ). (c) f __ 1 __. 2 2 2. 2. 31 1 6 ___. 4. a a 2 a a 3a 6. (d) f . 4() (). __ __. 4 ( ). __. 3 6 . 4. ___. 16. ___. 4. 6. Length (x y). Width (2x 3y). (a) Area (x y)(2x 3y) 2x2 3xy 2xy 3y2. 2x2 xy 3y2. (b) Perimeter 2[(x y) (2x 3y)] 2[3x 2y] 6x 4y 6. Chapter 1. 7. Length x cm Width (x 5) cm Height 2x cm. (a) Volume Length Width Height (x)(x 5)(2x) 2x3 10x2. (b) Surface area 2(x)(x 5) 4(2x)(x 5) 4(2x)(x). 2x2 10x 8x2 40x 8x2. 18x2 50x. 8. (i) d(4) the number of diagonals in a 4-sided polygon (ii) d(5) the number of diagonals in a 5-sided polygon. (4)2 3(4). d(4) ____ ____ 8 6 2. 2 2. (5)2 ____. 3(5) ___. d(5) ____ 25 ___.

10 15 ___. 10 5. 2 2 2 2 2. (6)2 ____. ____ 3(6) ___. 36 18. ___ 18. ___. d(6) 9. 2 2 2 2 2. d(3) 0 because a triangle has no diagonal. 9. If f (x) x 5, f (a2) 3f (a) 2 a2 5 3(a 5) 2. a2 5 3a 15 2. a2 3a 8. 10. f (x) x2 3x 6. (i) f ( 2t) ( 2t)2 3( 2t) 6 4t2 6t 6. (ii) f (t 2) (t 2)2 3(t 2) 6 t4 3t2 6. (iii) f (t 2) (t 2)2 3(t 2) 6 t2 4t 4 3t 6 6. t2 7t 16. (i) 4t2 6t 6 is of degree 2. (ii) t4 3t2 6 is of degree 4. (iii) t2 7t 16 is of degree 2. 11. V (r, h) __1 r2h. 3 1 142 21 1372 cm3. (i) V (r 14, h 21) __. 3. 1. (ii) V (r, h r) r r __. __ 2 1 r3. 3 3. 1. (iii) V (r 2h, h) (2h) h __. __ 2 4 h3. 3 3. 12. The dimensions of the base of the box are 24 2x and 18 2x, in cm.