8. (i) n3
− 15n2
(ii) −2m3 (iii) –3x3 (iv) 36y3
(v) −4q3 (vi) 4t3
9. (i) 20y3 (ii) 4n3 (iii) p3
10.(i) 3a3 (ii) 6a3 (iii) 6a3 4a2
− 13m2 − 10x2 + 19t2 − 4p2 (iv) 15q3
− 94y + 40 + 4q2
+ 23y2 + 16n2
+ 45n + 25 + 17x + 36 − 14q + 14 − 19y − 10
− 20t − 24 + 11n − 10
+ 10q2
− 23p + 14 + 15q
+ ab − 2a + 9a2 + 3b − 6
− 12ab + 15a − 2a2 − 1·5ab + 13·5a + − b + 9
(ii) x2 (iii) m2 (iv) x2
2. (i) (ii) 3. (i) 4. (i) 5. (i)
− 16 − 4
− 4 − 1 (x − 2) (x + 15)
(iii) (x + 100) (ii)
(ii) (ii)
(x − 3)(x + 3) (x − 5)(x + 5)
(iii) (n − 12)(n + 12) (2x − 1)(2x + 1) (5t − 10)(5t + 10)
(iii) (10)(x − 2)(x + 2) (4x − 7)(4x + 7) (3x − 13)(3x + 13)
(iii) (7y − 9)(7y + 9)
6. 16 − x2 7. 4 − w2 8. (i)
(9y − 14)(9y + 14)
(ii) (121)(x − 1)(x + 1) (iii) (−36)(2p − 1)(2p + 1) (iv) (3a − 4b)(3a + 4b) (v)
(−25)(2t − w)(2t + w) (vi) (11x − 12y)(11x + 12y)
9. Square 1 perimeter = 12; Square 2 perimeter = 4x
10.Square 1 perimeter = 4a; Square 2 perimeter = 4b
11.(i) 2(4y − 3)(4y + 3) (ii) 2(2x − 3)(2x + 3) (iii) 3(2y − 3)(2y + 3) (iv) 3(4y − 5)(4y + 5) (v) 2(9y − 11)(9y + 11) (vi) 5(2y − 3)(2y + 3)
Practice questions 14.3 1. (i) x2
(ii) x2 (iii) m2 (iv) x2
2. y2 3. (i)
(ii)
+ 10x + 24 + 12x + 20 + 8m + 15 − 11x + 28
+ 19y + 90 (x + 5) (x + 2)
(iii) (y + 6) (iv) (n + 2) (v)
4. (i)
(vi) (n − 2) (ii)
(p − 7)
(x + 3)(x + 1) (x + 1)(x + 2)
(iii) (n + 2)(n + 5) (iv) (x − 2)(x − 8)
5. (x + 3);(x + 4) 6. (i)
(ii)
(x + 4)(x + 1) (x − 5)(x − 3)
(iii) (q + 6)(q + 4) (iv) (x + 12)(x + 1)
+ 4b − 5
Practice questions 14.2 1. (i) x2
7. (i) + 53m − 20 (ii) 8. x2
(x + 4)(x + 2) (x − 2)(x − 1)
(iii) (m + 11)(m + 1) (iv) (w − 7)(w − 9) + 14x + 40
9. (i) 3(x + 5)(x + 2) (ii) 2(x + 3)(x + 4) (iii) 2(r − 5)(r − 3) (iv) 3(x − 2)(x − 1) (5x + 6)(x + 4) (5r + 2)(r + 3)
10.(i) (ii)
(iii) (2p + 5)(3p + 1) (iv) (2x + 1)(x + 7)
11.(3a − 7) and (a − 1) 12.(i)
(ii) 13.(i)
(5x + 4)(x + 2) (2x − 3)(x − 1)
(ii)
(iii) (3x + 1)(4x + 1) (iv) (4x − 3)(2x − 1) (5x − 4)(2x − 1) (11x − 1)(2x − 1)
(iii) (3n + 2)(4n + 3) (iv) (7x − 1)(7x − 1)
14.(3x − 2)(x + 1) 15.(6x + 5)(3x + 7)
Practice questions 14.4 1. (i) x2
(ii) x2 (iii) m2
2. y2 3. (i)
(ii)
− 5x − 14 + 5x − 24 + 2m − 24
− 4y − 32 (x − 2) (x + 4)
(iii) (m − 2) (iv) (n + 3) (v)
(vi) (n + 2)
4. (x − 6)(x + 2) 5. (i)
(ii)
6. 6x2 7. (i)
(ii)
(x + 6)(x − 1) (x − 3)(x + 1)
(iii) (m − 4)(m + 3) (iv) (w − 3)(w + 2) − 24
(8x − 3)(x + 6) (2p − 5)(p + 6)
(iii) (7x − 9)(x − 5) (iv) (5x + 9)(x − 9)
8. (3a − 1) and (a + 1) 9. (i)
(ii) 10.(i) (ii)
(iii) (4x + 5)(x − 5) (iv) (5x + 1)(x − 1) (2x − 1)(x + 3) (3x − 1)(x + 5)
(iii) (7n + 1)(n − 2) (iv) (3n − 1)(2n + 5)
11.(2x − 7) and (x + 4) 12.(4m + 5) and (m − 5)
Practice questions 14.5
1. (i) 5a +6 (ii) 5x − 2 (iii) 3y + 1 (iv) y − 2
2. (i) x +3 (ii) x − 8 (iii) x − 3
3. (i) m +2 (ii) 2x + 8 (iii) 2n − 6
4. (x − 3) 5. (m − 10)
Answer key 383
(2x + 1)(x − 3) (3n − 7)(2n + 7)
(x − 10)
6. 2x + 3 7. n + 2 8. x + 2
9. 2y + 5 10.(i)
_____ 3y + 2
(ii) n + 1 (iii) a − 4 (iv) y + 9
__ 4
5x
____ n + 4
____ a + 4
____ y + 5
11.(i) a + 4 (ii) x − 8
(iii) n − 8 (iv) p + 7
____ x − 7
12.t + 18 13.3x + 4 14.5x + 7 15.5x + 4
Practice questions 14.6
1. (i) x = −5, x = 1 (ii) x = −2, x = −1
2. (i) x = −2, x = 3 (ii) x = −2·7, x = 0·7
3. (i) y = −1, y = −2 (ii) b = 4, b = −11 (iii) b = 12, b = −5 (iv) x = −2, x = −3
4. (i) x = −2, y = −7 (ii) x = −1, x = −20 (iii) x = −3, x = 6
(iv) x = 7
5. (i) x = −2, x = 4 (ii) x = 0·5, x = 1
__ 3, x = −7
(iii) x = −5 (iv) b = 2
___ 3
__ 2, x = −3
6. (i) m = −3 (ii) m = −4 (iii) x = −12 (iv) n = 8
7. (i) y = −3 (ii) w = −2 (iii) x = 5 (iv) x = 5
8. (i) y = 1
__ 3, b = 2
__ 2, m = 5
__ 7, n = −8
__ 3, x = −3
__ 2, x = −5
(ii) y = 6, y = −8
__ 3, y = 2
9. (i) x = −2, x = 3 (ii) x = 6, x = 3 (iii) x = −1, x = −4 (iv) x = 4, x = 7
10.(i) (y)(y + 4) = 780 (ii) Seán is 26 years old
11.(i) h = 128 (iii) 5 seconds
12.(i) €7 000 (ii) 6 months
13.(i) k2 − 12k + 27 (ii) k = 9, k = 3
14.(i) n = 8 (ii) 6, 8
15.(i) 4x2 + 26x (ii) Width = 1⋅5 m
__ 5 , x = 12
__ 3, m = 4
__ 5
___ 7
__ 2, y = −3
__ 3, w = 1
__ 2
__ 2
____ n − 6
____ p + 2
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