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Chapter 3 More about Factorization
Chapter 3
3.1
More about Factorization
WARM-UP EXERCISE
1. Find the factors of each of the following numbers.
(a) 12
(b) 72
2. Expand the following expressions.
(a) (x  7) 2
(b) (3x  4y) 2
3. Expand the following expressions.
(a) (2a  5) 2
(b) (6a  2b) 2
4. Expand the following expressions.
(a) (x  4y)(x  4y)
(b) (9x  7y)(9x  7y)
5. Expand the following expressions.
(a) (x  2)(3x  4)
(b) (3x  2y)(4x  3y)
6. Express the following expressions in positive indices.
(a) (
6 x 1
3x 2
)2
(b)
7( x 2 y 4 ) 3
y 2 x
BUILD-UP EXERCISE
Exercise 3A
 Elementary Set
Level 1

1. Factorize the following expressions.
(a) 2a  4
(b) 3a  3
(c) 5  5a
(d) 18a  9
(e) 4a  26
(f) 70  25a
Ex.3A Elementary Set
[ This part provides two extra sets of questions for each exercise in the textbook, namely Elementary Set and
Advanced Set. You may choose to complete any ONE set according to your need. ]
3.2
New Trend Mathematics S3A — Junior Form Supplementary Exercises
2. Factorize the following expressions.
(a) 4a  8
(b) 3a  9
(c) 4  8b
(d) 8a  2b
(e) 3ab  12
(f) 16  6ab
3. Factorize the following expressions.
(a) 4x  12y  8
(b) 9x  27y  18z
(c) 5x  10y  20z
(d) 3x  18y  27z
(e) 16x  4y  20z
(f) 6x  10y  22z
4. Factorize the following expressions.
(a) 5a  10ab
(b) 4a  8ab
(c) 12ab  20a
(d) 18ab  9bc
(e) 28ab  49b2
(f) 50ab  60b2
Ex.3A Elementary Set
5. Factorize the following expressions.
(a) 4a 2b  8ab 2
(b) 25ab 2  100a 2b
(c) 4a 3  10a2b
(d) 2ab  4a 2b2
(e) 3a 2b  9b 2c2
(f) 10a 2bc 2  20ab 2c
6. Factorize the following expressions.
(a) b(a  3)  2(a  3)
(b) a(a  1)  4b(a  1)
(c) 15(a  b)  b(b  a)
(d) 8(a  2b)x  (a  2b)y
(e) (a  12)2  5b(12  a)
(f) 2b(a2  b)  (a2  b) 2
7. Factorize the following expressions.
(a) x  y  ax  ay
(b) 2b  2  ab  a
(c) xy  x  2y  2
(d) 2x  ax  2y  by
(e) x  y  2xz  2yz
(f) 3ax  3ay  x  y
8. Factorize the following expressions.
(a) p 2  9
(b) 100  q 2
(c) p 2  a2b 2
(d) 16p2  1
(e) 5q 2  45
(f) 3p 2  12
Chapter 3 More about Factorization
3.3
Level 2
(a) m2  2m  1
(b) m2  4m  4
(c) m2  8m  16
(d) m2  20m  100
(e) 2m2  8m  8
(f) 5m2  45  30m
10. Factorize the following expressions.
(a) a 2b  ab2  5a  5b
(b) a  2ab  21b 2  42b 3
(c) 2a 4  9a 2  8a 2b  36b
(d) 56ax  4b2  32bx  7ab
(e) b 2x  15b  3abx 2  45ax
(f) 24by  3ax  2bx  36ay
Ex.3A Elementary Set
9. Factorize the following expressions.
11. (a) Factorize the following expressions.
(i) 16x 2  9y 2  24xy
(ii) 4x 2  28x  49
(b) Using the results of (a), factorize (16x2  9y 2  24xy)  4(4x 2  28x  49).
12. (a) Factorize p 2  4pq  4q 2.
(b) Hence factorize (m  1) 2  4(m  1)(5n)  4(5n) 2.
 Advanced Set
Level 1

(a) 4a  8
(b) 3a  9b
(c) 27ab  45
(d) 4  16x
(e) 36x  12y  42
(f) 81x  54y  135z
2. Factorize the following expressions.
(a) 40a  20ab
(b) 32a  27ab
(c) 5xy  10yz
(d) 30a 2  9a 2c 2
(e) 25x 3  50x 2y
(f) 7axy  49a 2x2y
3. Factorize the following expressions.
(a) a(b  1)  3(b  1)
(c) 5p(3q  2)  10(3q  2)
(e) 2pr  2ps  r  s
(b) 2x(y  1)  3(1  y)
2
(d) 2  2y  x  xy
(f) ax  bx  ay  by
Ex.3A Advanced Set
1. Factorize the following expressions.
3.4
New Trend Mathematics S3A — Junior Form Supplementary Exercises
4. Factorize the following expressions.
(a) x 2  4
(b) x 2  81
(c) 16  a 2b 2
(d) 25x 2  64y2
(e) 8x 2  50
(f) 4x 2  81y 4
Level 2
5. Factorize the following expressions.
(a) 6ax  b  3bx  2a
(b) 6x 2  3xz  2xy  yz
(c) 10ax  12by  20bx  6ay
(d) 20abx 2  20  16ax  25bx
(e) 12a 2xy  10  8ay  15ax
(f) 18wx 2  20yz 2  30x 2z 2  12wy
6. Factorize the following expressions.
(a) 200y 2  32x 2
(b) 81x 2y  16y(x  y) 2
(c) 256  81x 4
(d) (x  y) 4  (x  y) 4
Ex.3A Advanced Set
7. Factorize the following expressions.
(a) m 2  6m  9
(b) 8m  16m 2  1
(c) 9  12m  4m 2
(d) 3m 2  6m  3
(e) 8m 2  40m  50
(f) 18m 2  24m  8
8. Factorize the following expressions.
(a) 4x 2  9y 2  12xy
(b) a 2b 2  2abc  c 2
(c) 36x 2y 2  25  60xy
(d) 28a 2  7b2  28ab
(e) 12p 2  27q2  36pq
(f) 36x 2  4y 2z 2  24xyz
9. (a) Factorize the following expressions.
(i) 16x 2  24xy  9y 2
(ii) z 2  8z  16
(b) Using the results of (a), factorize (16x 2  24xy  9y2) + 8(4x  3y)  16.
10. (a) Factorize x4  y 4 .
(b) Hence factorize x4  2x2z  y 4  2y2z.
11. (a) Factorize the following expressions.
(i) 3y 2  12y  12
(ii) y 3  4y 2  4y
(b) Using the results of (a), factorize y 3  7y2  16y  12.
3.5
12. Factorize the following expressions.
(a) (2x  y) 2  y2  4x2
(b) z 2  (y 2  25x 2  10xy)
(c) 48  27a 2  36ab  12b 2
(d) 9w 2  24wz  16z 2  36x2  36xy  9y2
Exercise 3B
 Elementary Set
Level 1
Ex.3A Advanced Set
Chapter 3 More about Factorization

1. In each of the following, find the numbers p and q.
(a) pq  2, p  q  3
(b) pq  8, p  q  6
(c) pq  14, p  q  9
(d) pq  10, p  q  3
2. Kent factorizes the quadratic polynomials by using cross multiplication. Fill in the blanks
with suitable expressions, and find the correct pair of factors to factorize the following
expressions.
(a) x 2  5x  6
1
6
Sum of the cross products  (
Therefore, (
1
6
2
3
)(
)(
) and (
 x 2  5x  6  (
2
3
)(
)
) are the pair of factors.
)(
)
(b) y 2  7y  18
y
y
1
18
Sum of the cross products  (
Therefore, (
2
9
)(
3
6
)(
) and (
 y 2  7y  18  (
)(
6
3
9
2
18
1
)(
)(
)(
)
) are the pair of factors.
)
(c) z 2  2z  15
z
z
(
(
)(
)(
)(
)(
)(
)(
)
)
Sum of the cross products  (
)(
)(
)(
)
Therefore, (
 z  2z  15  (
2
) and (
)(
) are the pair of factors.
)
Ex.3B Elementary Set
x
x
3.6
New Trend Mathematics S3A — Junior Form Supplementary Exercises
3. Factorize the following expressions.
(a) a 2  8a  7
(b) a 2  14a  13
(c) b 2  12b  20
(d) b 2  12b  27
(e) c 2  14c  48
(f) c 2  16c  55
4. Factorize the following expressions.
(a) x 2  9x  14
(b) x 2  10x  24
(c) y 2  13y  22
(d) y 2  17y  16
(e) z 2  11z  24
(f) z 2  25z  100
5. Factorize the following expressions.
(a) x 2  x  12
(b) x 2  2x  3
(c) y 2  3y  10
(d) y 2  14y  15
(e) z 2  3z  54
(f) z 2  10z  144
Ex.3B Elementary Set
6. Factorize the following expressions.
(a) p 2  10p  11
(b) p 2  4p  21
(c) q 2  7q  60
(d) q 2  8q  20
(e) r 2  12r  64
(f) r 2  19r  150
Level 2
7. Factorize the following expressions.
(a) 200  m 2  30m
(b) 13m  14  m 2
(c) 18  7m  m 2
(d) n 2  5n  6
(e) 42  n  n2
(f) 10n  n 2  75
8. Factorize the following expressions.
(a) a(a  13)  36
(b) a 2  4(a  15)
(c) 3(5a  12)  a 2
(d) (a  13)(a  1)  49
(e) (a  6)(a  13)  20
(f) 14  (a  15)(a  10)
9. (a) If x 2  ax  6  (x  2)(x  b), find the values of a and b.
(b) Hence factorize (x  b)(x  5)  20a.
Chapter 3 More about Factorization
 Advanced Set
Level 1
3.7

1. In each of the following, find the numbers p and q.
(a) pq  10, p  q  7
(b) pq  24, p  q  10
(c) pq  14, p  q  5
(d) pq  24, p  q  5
2. In the diagram below, circle the factors of x 2  7x  30.
x
x
1
30
2
15
3
10
5
6
6
5
10
3
15
2
30
1
(a) a 2  4a  3
(b) a 2  12a  32
(c) b 2  9b  18
(d) b 2  7b  10
(e) c 2  23c  120
(f) c 2  19c  90
4. Factorize the following expressions.
(a) x 2  4x  5
(b) x 2  18x  19
(c) y 2  6y  27
(d) y 2  y  2
(e) z 2  2z  24
(f) z 2  4z  45
Level 2
5. Factorize the following expressions.
(a) 6  a  a 2
(b) b 2  100  29b
(c) 9c  22  c2
(d) 15  x 2  8x
(e) y 2  36  5y
(f) 6z  72  z 2
6. Factorize the following expressions.
(a) 14p  40  p 2
(b) 30  q  q2
(c) 2r  r 2  48
(d) 14  s 2  13s
(e) 100  t 2  15t
(f) 64  u 2  16u
7. Factorize the following expressions.
(a) a(a  12)  35
(b) a 2  5(3a  10)
(c) 7(2b  21)  b 2
(d) (b  7)(b  8)  12
(e) 180  (c  6)(c  9)
(f) (5  c)(4  c)  90
Ex.3B Advanced Set
3. Factorize the following expressions.
3.8
New Trend Mathematics S3A — Junior Form Supplementary Exercises
8. (a) Factorize the following expressions.
Ex.3B Advanced Set
(i) y 2  5y  4
(ii) y 2  13y  12
(b) Using the results of (a), factorize (y 3  5y2  4y)  (2y2  26y  24).
9. (a) If x 2  ax  96  (x  b)(x  12), find the values of a and b.
(b) Hence factorize (a  y)(y  b)  75.
Exercise 3C
 Elementary Set
Level 1

1. In the diagram below, circle the factors of 3x 2  11x  4.
x
3x
1
4
2
2
1
4
4
1
2
2
4
1
2. In the diagram below, circle the factors of 2x 2  7x  6.
x
2x
1
6
2
3
3
2
1
6
6
1
2
3
3
2
6
1
Ex.3C Elementary Set
3. In the diagram below, circle the factors of 6x 2  11x  10.
x
6x
2x
3x
1
10
2
5
5
2
10
1
1
10
2
5
5
2
10
1
4. Factorize the following expressions.
(a) 2x 2  x  1
(b) 5x 2  4x  1
(c) 6y 2  5y  1
(d) 4y 2  5y  1
(e) 10z 2  7z  1
(f) 27z 2  12z  1
5. Factorize the following expressions.
(a) 2a 2  3a  2
(b) 3a 2  8a  5
(c) 3b 2  5b  2
(d) 2b 2  5b  7
(e) 5c 2  12c  7
(f) 11c 2  14c  3
Chapter 3 More about Factorization
3.9
6. Factorize the following expressions.
(a) 2p 2  9p  9
(b) 4p 2  7p  3
(c) 8q 2  3q  5
(d) 6q 2  23q  7
(e) 10r 2  3  r
(f) r  2  15r 2
(a) 2m 2  5m  12
(b) 5m 2  27m  18
(c) 31n  12  7n 2
(d) 11n  4  3n 2
(e) 3k 2  24k  45
(f) 20  3k 2  4k
Level 2
8. Factorize the following expressions.
(a) 9s 2  5s  4
(b) 6s 2  11s  21
(c) 8t 2  6t  27
(d) 4t 2  8t  45
(e) 10u 2  21u  9
(f) 12u 2  36  11u
Ex.3C Elementary Set
7. Factorize the following expressions.
9. Factorize the following expressions.
(a) 6x 2  3x  9
(b) 12x 2  32x  20
(c) 18y 2  6y  4
(d) 44  102y  20y 2
(e) 40z  66z 2  6
(f) 2z(4z  1)  10
10. (a) Factorize 6p2  13p  5.
(b) Hence factorize 6(2q  3) 2  13(2q  3)  5.

1. In the diagram below, circle the factors of 9x 2  47x  10.
x
9x
3x
3x
1
10
2
5
5
2
10
1
1
10
2
5
5
2
10
1
2. In the diagram below, circle the factors of 16x 2  18x  9.
x
16x
2x
8x
4x
4x
1
9
3
3
9
1
1
9
3
3
9
1
Ex.3C Advanced Set
 Advanced Set
Level 1
3.10
New Trend Mathematics S3A — Junior Form Supplementary Exercises
3. (a) Assume that 2x 2  x  5 can be factorized by using the cross multiplication, what should
be the sum of the cross products?
(b) Fill in the blanks with suitable expressions.
For 2x 2  x  5,
x
2x
1
5
Sum of the cross products  (
1
5
5
1
)(
)(
5
1
)(
)
(c) Based on the result of (b), is the assumption in (a) correct?
4. Factorize the following expressions.
(a) 5x 2  14x  3
(b) 7x 2  36x  5
(c) 2a 2  a  3
(d) 3p 2  11  8p
(e) 7x 2  7  4x
(f) 2  7a  5a 2
5. Factorize the following expressions.
Ex.3C Advanced Set
(a) 6p 2  7p  5
(b) 10a 2  7a  3
(c) 13p  3  10p 2
(d) 3  4m 2  4m
(e) 10n  3  12n 2
(f) 2  5q  18q 2
6. Factorize the following expressions.
(a) 4x 2  20x  24
(b) 3x 2  21x  30
(c) 28x  84  7x 2
(d) 30  4x  2x 2
(e) 120  10x  5x 2
(f) 64  4x 2  6x
Level 2
7. Factorize the following expressions.
(a) 18a 2  3a  10
(b) 21y 2  y  36
(c) 24a 2  35  22a
(d) 4p 2  9p  6
(e) p  20  12p 2
(f) 18  10q 2  57q
8. Factorize the following expressions.
(a) 30x 2  35x  10
(b) 20x 2  76x  16
(c) 15x  18  12x 2
(d) 27p  6p 2  15
(e) 4x(1  4x)  30
(f) 21  6p(3  8p)
3.11
9. (a) Factorize (x  1)(x  6)  8.
(b) Hence factorize (2y 2  5y  1)(2y 2  5y  6)  8.
10. (a) Factorize 16y 2  16y  4.
(b) Hence, or otherwise, factorize (16x 4  16x 2  4)  49x2.
Exercise 3D
 Elementary Set
Level 1
Ex.3C Advanced Set
Chapter 3 More about Factorization

1. Factorize the following quadratic polynomials in two variables by using the diagram below.
y
14y
2y
7y
y
14y
2y
7y
Sum of the cross products  15xy
9xy
15xy
9xy
x
x
(a) x  9xy  14y  (
2
2
)(
(b) x 2  15xy  14y 2  (
)
)(
)
x
8x
2x
4x
y
25y
5y
5y
25y
y
y
25y
5y
5y
25y
y
3. Factorize the following expressions.
(a) x 2  xy  2y 2
(b) x 2  4xy  3y 2
(c) 5m 2  4mn  n 2
(d) m 2  12mn  13n 2
(e) u 2  11v2  10uv
(f) 3u 2  v 2  2uv
4. Factorize the following expressions.
(a) a 2  5ab  6b 2
(b) a 2  8ab  9b 2
(c) 10p 2  7pq  q 2
(d) p 2  25q 2  10pq
(e) 3rs  10s 2  r 2
(f) 8r 2  s 2  2rs
5. Factorize the following expressions.
(a) x 2  6xy  16y 2
(b) 18x 2  9xy  y 2
(c) p 2  11pq  30q2
(d) 70p 2  q 2  19pq
(e) 14st  s 2  24t 2
(f) 5st  t 2  36s 2
Ex.3D Elementary Set
2. In the diagram below, circle the factors of 8x 2  30xy  25y 2.
3.12
New Trend Mathematics S3A — Junior Form Supplementary Exercises
Level 2
6. Factorize the following expressions.
Ex.3D Elementary Set
(a) 5a 2  16ab  11b 2
(b) 2a 2  21ab  19b2
(c) 24m 2  2mn  5n 2
(d) 5m 2  23mn  12n 2
(e) 13uv  3v 2  30u 2
(f) 15u 2  8uv  12v 2
7. Factorize the following expressions.
(a) 5x 2  30xy  35y 2
(b) 15p 2  6pq  21q2
(c) 14p 2  49pq  42q2
(d) 4x 2  12xy  40y 2
(e) 30ab  4a 2  100b2
(f) 20a 2  105b 2  40ab
8. (a) Factorize 6x 2  13xy  28y2.
(b) Hence factorize 6x 2  13xy  28y 2  10x  35y.
 Advanced Set
Level 1

1. In the diagram below, circle the factors of 6x 2  xy  15y 2.
x
6x
2x
3x
y
15y
3y
5y
5y
3y
15y
y
y
15y
3y
5y
5y
3y
15y
y
2. Factorize the following expressions.
Ex.3D Advanced Set
(a) m 2  6mn  5n 2
(b) 3x 2  2xy  y 2
(c) x 2  5xy  14y 2
(d) 8a 2  6ab  b 2
(e) u 2  17v 2  16uv
(f) p 2  32q 2  4pq
3. Factorize the following expressions.
(a) 2x 2  23xy  11y2
(b) 5x 2  8xy  13y 2
(c) 2a 2  11ab  21b 2
(d) 27p 2  15pq  2q2
(e) 7a 2  3b 2  20ab
(f) 11pq  10q 2  3p 2
4. Factorize the following expressions.
(a) 11u 2  19uv  8v 2
(b) 5u 2  43uv  18v 2
(c) 6m 2  17mn  12n 2
(d) 24m 2  7n 2  38mn
(e) 11r 2  8s 2  18rs
(f) 16r 2  5s 2  18rs
Chapter 3 More about Factorization
3.13
5. Factorize the following expressions.
(a) 6a 2  5ab  4b 2
(b) 8a 2  18ab  81b2
(c) 20x 2  11xy  42y 2
(d) 15y 2  17yz  4z 2
(e) 9u 2  22uv  15v 2
(f) 7uv  3v 2  6u 2
(a) 9xy  54y 2  3x 2
(b) 100y 2  5x2  5xy
(c) 24(r 2  2t 2)  88rt
(d) 10r 2  34rt  28t 2
(e) 24a 2  20b2  28ab
(f) 18b 2  16a2  24ab
Level 2
Ex.3D Advanced Set
6. Factorize the following expressions.
7. (a) Factorize the following expressions.
(i) 6x 2  xy  2y 2
(ii) 2x 2  xy  2x  y
(b) Using the results of (a), factorize 10x 2  xy  2y 2  4x  2y.
8. (a) Factorize the following expressions.
(i) 4x 2  12xy  9y 2
(ii) 9y 2  24yz  16z2
(b) Using the results of (a), factorize 4(4x 2  12xy  9y2)  25(9y 2  24yz + 16z 2).
Exercise 3E
 Elementary Set
Level 1

1. Fill in the blanks with ‘’ or ‘’ to make the equalities hold.
□ b)(a2 □ ab □ b2)
(b) a 3
□ b3  (a □ b)(a2  ab □ b2)
2. Find the values of p and q in each of the following.
(a) x 3  1 728  (x  12)(x 2  px  q)
(b) x 3  512  (x  p)(x2  qx  64)
(c) 343x 3  1  (px  1)(qx 2  7x  1)
3. Factorize the following expressions.
(a) x 3  2 3
(c) x 3  10 3
(b) x 3  5 3
Ex.3E Elementary Set
(a) a 3  b 3  (a
3.14
New Trend Mathematics S3A — Junior Form Supplementary Exercises
4. Factorize the following expressions.
(a) y 3  216
(b) 125  y 3
(c) y 3  8
5. Factorize the following expressions.
(a) 2 3x 3  1
(b) (15x) 3  1
(c) 216x 3  1
6. Factorize the following expressions.
(a) x 3  (9y) 3
(b) (12x) 3  y 3
(c) x 3  27y 3
Ex.3E Elementary Set
7. Factorize the following expressions.
(a) (4y) 3  113
(b) 16 3  (9y) 3
(c) 1 000y 3  343
8. Factorize the following expressions.
(a) 2a 3  2b 3
(b) 4a 3  32b3
(c) 54a 3  250b 3
Level 2
9. Factorize the following expressions.
(a) ab 3  ac 3
(b) 9a 3  72
(c) 6ab 3  48ac 3
(d) a 3b 2  64b 2c 3
10. Factorize the following expressions.
(a) 6 3  (4  3x) 3
(b) (2x) 3  (2  x) 3
(c) 125x 3  (x  y) 3
(d) (5a  6) 3  729
Ex.3E Advanced Set
 Advanced Set
Level 1

1. Factorize the following expressions.
(a) x 3  6 3
(c) 4 3x 3  1
(b) 5 3x 3  1
Chapter 3 More about Factorization
3.15
2. Factorize the following expressions.
(a) x 3  8
(b) x 3  27
(c) 1 000x 3  1
3. Factorize the following expressions.
(a) x 3  (20y) 3
(b) (11x) 3  y3
(c) 125x 3  y 3
4. Factorize the following expressions.
(a) (11x) 3  93
(b) 64x 3  27
(c) 216  125x3
5. Factorize the following expressions.
(a) 4x 3  4y 3
(b) 5a 3  40b3
6. Factorize the following expressions.
(a) 2x 3  128
(b) 5 000  5x 3
(c) 48x 3  6
(d) 81x 3  24
Level 2
7. Factorize the following expressions.
(a) mn 3  mp 3
(b) 2x 2y 3  16x 5
(c) 125p 4q  pq 4
(d) 54u 6v 2  250u 3v 5
8. Factorize the following expressions.
(a) 15 3  (x  5) 3
(b) 64y 3  (4  y) 3
(c) x 3  y 3  (3x 2y  3xy 2)
(d) (a  2b) 3  (3a  b)3
9. (a) Factorize a 6  b 6 .
[ Hint: a 6  b 6  (a 3) 2  (b 3)2 ]
(b) Hence factorize (x  y) 6  (x  y) 6.
10. (a) Factorize 8x 3  27.
(b) Hence factorize 16x 3  4x  48.
Ex.3E Advanced Set
(c) 189s 3  56t 3
3.16
New Trend Mathematics S3A — Junior Form Supplementary Exercises
CHAPTER TEST
(Time allowed: 1 hour)
Section A (1) [ 3 marks each ]
1. Factorize the following expressions.
(a) 30ab  15a2b
(b) x 2  14xy  49y 2
2. Factorize xy  8y  9x  72.
3. Factorize 24t 2  2t  1.
4. Factorize 3u 2  14u  5.
5. Factorize 3a 2  2ab  b 2.
6. Factorize 1  27q 3.
Section A (2) [ 6 marks each ]
7. Factorize 10x 2  12x 3  8x.
8. Factorize 16a 2  15b 2  8ab.
9. Factorize (x  2) 2  4(x 2  4x  12).
10. Factorize 27s 3  125t 3  6s  10t.
Section B
11. (a) Factorize 3x 2  8x  80.
(4 marks)
(b) Factorize x 3  64.
(3 marks)
(c) Hence factorize x 3  6x2  16x  96.
(6 marks)
Chapter 3 More about Factorization
3.17
Multiple Choice Questions [ 3 marks each ]
12. Which of the following must be correct?
17. 16  6a  a2 
I. a 2  b 2  (a  b)(a  b)
A. (a  4) 2.
II. (a  b)  a  2ab  b
2
B. (a  4) 2.
III. (a  b)  a  2ab  b
2
2
2
2
2
C. (a  8)(a  2).
A. II only
D. (a  8)(a  2).
□
B. I and III only
C. II and III only
D. I, II and III
□
18. 13x  30  x 2 
A. (x  15)(x  2).
B. (x  15)(x  2).
13. If ax 2  y 2  (2x  y)(y  2x), then a 
C. (x  3)(x  10).
A. 4.
D. (x  3)(x  10).
B. 2.
C. 2.
D. 4.
□
□
19. 16u 2  60v2  16uv 
A. (u  12v)(16u  5v).
14. xy  y  1  x 
B. 2(u  6v)(8u  5v).
A. (x  1)(y  1).
C. 4(u  5v)(4u  3v).
B. (x  1)(y  1).
D. 4(2u  3v)(2u  5v).
C. (1  x)(y  1).
D. 2xy(1  x).
□
□
20. (x  1) 2  2x 2  5x  3 
A. (x  1)(x  2).
15. a 2b 3c  bc3 
B. (x  1)(2x  3).
A. a 2b 2c 2.
C. (x  1) 2(2x  3).
B. bc 3(a  1)(a  1).
C. bc(ab  c)(ab  c).
D. bc(ab  c) 2.
D. (x  2)(2x  3).
□
21. Which of the following has the factor
2x  1?
16. (x  6)(7  x)  4x 
A. 4x 3  2x 2
A. (x  3)(x  14).
B. 6x 2  x  2
B. (x  3)(x  14).
C. (x  3)(x  14).
D. (x  3)(x  14).
□
C. 2x 2  1
□
D. 4xy  2y  6x  3
□
3.18
New Trend Mathematics S3A — Junior Form Supplementary Exercises
22. Which of the following does not have the
factor 3x  2?
26. Which of the following have the factor
3x  y?
A. 3x 2  4
I. 3ax  3by  ay  9bx
B. 9x 2  4x
II. 27x 3  y 3
C. (9x 3  4x)  (18x  12)
III. 27x 3  y 3
D. (9x 3  4x)  (18x  12)
□
A. I and II only
B. I and III only
23. It is known that 3x 2  ax  6, where a is
an integer, can be factorized by using the
cross multiplication. Which of the
following is/are not the possible value(s)
of a?
I. 7
II. 3
III. 9
A. II only
B. III only
C. I and III only
D. II and III only
□
24. Which of the following must be correct?
I. a 3  b 3  (a  b)(a2  2ab  b 2)
II. a 3  b 3  (a  b)(a2  ab  b2)
III. a 2  b 2  (a  b)(a  b)
A. I only
B. II only
C. III only
D. None of the above
□
25. 8x 3  y 3 
A. (2x  y)(4x 2  2xy  y2).
B. (2x  y)(4x 2  xy  y2).
C. (2x  y)(4x 2  2xy  y2).
D. (2x  y)(4x 2  2xy  y2).
□
C. II and III only
D. I, II and III
□