S2-4.1-Ch4多項式因式分解

Authored by Hoi Wong

Mathematics

9th Grade

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MULTIPLE CHOICE QUESTION

15 mins • 1 pt

49.   18x – 24y =
       A.   –6(3x – 4y)。
       B.    –6(3x + 4y)。
       C.   6(3x – 4y)。
       D.   6(3x + 4y)。

Answer explanation

49.     18x – 24y
            = 6(3x) – 6(4y)
            = 6(3x – 4y)
            ∴     答案是C。

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

50.   –3e – 7de =
       A.   –e(3 – 7d)。
       B.    –e(3 + 7d)。
       C.   e(3 – 7d)。
       D.   e(3 + 7d)。

Answer explanation

50.     –3e – 7de
            = –e(3) + (–e)(7d)
            = –e(3 + 7d)
            ∴     答案是B。

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

51.   –12xy – 18xz + 24x² =
       A.   6x(4x + 2y + 3z)。
       B.    6x(4x + 2y – 3z)。
       C.   6x(4x – 2y + 3z)。
       D.   6x(4x – 2y – 3z)。

Answer explanation

51.     –12xy – 18xz + 24x²
            = 6x(–2y – 3z + 4x)
            = 6x(4x – 2y – 3z)
            ∴     答案是D。

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

52.   (3a + 4b)² – 6a – 8b =
       A.   (3a + 4b)(3a + 4b + 2)。
       B.    (3a + 4b)(3a + 4b – 2)。
       C.   (3a + 4b)(3a – 4b + 2)。
       D.   (3a + 4b)(3a – 4b – 2)。

Answer explanation

52.     (3a + 4b)² – 6a – 8b
         = (3a + 4b)² – 2(3a + 4b)
         = (3a + 4b)(3a + 4b – 2)
            ∴     答案是B。

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

53.   pq – qr – 4p + 4r =
       A.   (p + r)(q + 4)。
       B.    (p + r)(q – 4)。
       C.   (p – r)(q + 4)。
       D.   (p – r)(q – 4)。

Answer explanation

53.     pq – qr – 4p + 4r
            = q(p – r) – 4(p – r)
            = (p – r)(q – 4)
            ∴     答案是D。

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

54.   ab – ac + 2bc – 2b² =
       A.   (a + 2b)(b – c)。
       B.    (a + 2b)(c – b)。
       C.   (a – 2b)(b – c)。
       D.   (a – 2b)(c – b)。

Answer explanation

54.     ab – ac + 2bc – 2b²
            = ab – 2b² – ac + 2bc
            = b(a – 2b) – c(a – 2b)
            = (a – 2b)(b – c)
            ∴    答案是C。

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

55.   x² – 5x + xy – xz – yz – 5y =
       A.   (x + y)(x – z + 5)。
       B.    (x + y)(x – z – 5)。
       C.   (x – y)(x – z + 5)。
       D.   (x – y)(x – z – 5)。

Answer explanation

55.   x² – 5x + xy – xz – yz – 5y
    = x² – xz – 5x + xy – yz – 5y
    = x(x – z – 5) + y(x – z – 5)
    = (x + y)(x – z – 5)
            ∴    答案是B。

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S2-4.1-Ch4多項式因式分解

49.   18x – 24y =
       A.   –6(3x – 4y)。
       B.    –6(3x + 4y)。
       C.   6(3x – 4y)。
       D.   6(3x + 4y)。

49.     18x – 24y
            = 6(3x) – 6(4y)
            = 6(3x – 4y)
            ∴     答案是C。

50.   –3e – 7de =
       A.   –e(3 – 7d)。
       B.    –e(3 + 7d)。
       C.   e(3 – 7d)。
       D.   e(3 + 7d)。

50.     –3e – 7de
            = –e(3) + (–e)(7d)
            = –e(3 + 7d)
            ∴     答案是B。

51.   –12xy – 18xz + 24x² =
       A.   6x(4x + 2y + 3z)。
       B.    6x(4x + 2y – 3z)。
       C.   6x(4x – 2y + 3z)。
       D.   6x(4x – 2y – 3z)。

51.     –12xy – 18xz + 24x²
            = 6x(–2y – 3z + 4x)
            = 6x(4x – 2y – 3z)
            ∴     答案是D。

52.   (3a + 4b)² – 6a – 8b =
       A.   (3a + 4b)(3a + 4b + 2)。
       B.    (3a + 4b)(3a + 4b – 2)。
       C.   (3a + 4b)(3a – 4b + 2)。
       D.   (3a + 4b)(3a – 4b – 2)。

52.     (3a + 4b)² – 6a – 8b
         = (3a + 4b)² – 2(3a + 4b)
         = (3a + 4b)(3a + 4b – 2)
            ∴     答案是B。

53.   pq – qr – 4p + 4r =
       A.   (p + r)(q + 4)。
       B.    (p + r)(q – 4)。
       C.   (p – r)(q + 4)。
       D.   (p – r)(q – 4)。

53.     pq – qr – 4p + 4r
            = q(p – r) – 4(p – r)
            = (p – r)(q – 4)
            ∴     答案是D。

54.   ab – ac + 2bc – 2b² =
       A.   (a + 2b)(b – c)。
       B.    (a + 2b)(c – b)。
       C.   (a – 2b)(b – c)。
       D.   (a – 2b)(c – b)。

54.     ab – ac + 2bc – 2b²
            = ab – 2b² – ac + 2bc
            = b(a – 2b) – c(a – 2b)
            = (a – 2b)(b – c)
            ∴    答案是C。

55.   x² – 5x + xy – xz – yz – 5y =
       A.   (x + y)(x – z + 5)。
       B.    (x + y)(x – z – 5)。
       C.   (x – y)(x – z + 5)。
       D.   (x – y)(x – z – 5)。

55.   x² – 5x + xy – xz – yz – 5y
    = x² – xz – 5x + xy – yz – 5y
    = x(x – z – 5) + y(x – z – 5)
    = (x + y)(x – z – 5)
            ∴    答案是B。

56.
3(2m–5n)² + (5n –2m)(5 –m)
= 3(2m –5n)²–(2m –5n)(5–m)
= (2m–5n)[3(2m–5n)–(5–m)]
= (2m –5n)(6m –15n –5 +m)
= (2m –5n)(7m –15n –5)
∴ 答案是D。

57.   下列哪些多項式彼此間有公因式？
       I.     a² – bc + ab – ac
       II.    b² – ac + bc – ab
       III. c² + ab – bc – ac
       A.   只有I及II
       B.    只有I及III
       C.   只有II及III
       D.   I、II及III

58.  下列何者是 (x – 1)² + 2(x – 1) + x(x + 1)的因式？
       I.     x – 1
       II.    x + 1
       III. 2x – 1
       A.   只有I及II
       B.    只有I及III
       C.   只有II及III
       D.   I、II及III

58.
(x – 1)² + 2(x – 1) + x(x + 1)
= (x – 1)[(x – 1) + 2] + x(x + 1)
= (x – 1)(x + 1) + x(x + 1)
= (x + 1)[(x – 1) + x]
= (x + 1)(2x – 1)
∴     II及III是該多項式的因式。
∴     答案是C。

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S2-4.1-Ch4多項式因式分解

49. 18x – 24y = A. –6(3x – 4y)。 B. –6(3x + 4y)。 C. 6(3x – 4y)。 D. 6(3x + 4y)。

49. 18x – 24y = 6(3x) – 6(4y) = 6(3x – 4y) ∴ 答案是C。

50. –3e – 7de = A. –e(3 – 7d)。 B. –e(3 + 7d)。 C. e(3 – 7d)。 D. e(3 + 7d)。

50. –3e – 7de = –e(3) + (–e)(7d) = –e(3 + 7d) ∴ 答案是B。

51. –12xy – 18xz + 24x2 = A. 6x(4x + 2y + 3z)。 B. 6x(4x + 2y – 3z)。 C. 6x(4x – 2y + 3z)。 D. 6x(4x – 2y – 3z)。

51. –12xy – 18xz + 24x2 = 6x(–2y – 3z + 4x) = 6x(4x – 2y – 3z) ∴ 答案是D。

52. (3a + 4b)2 – 6a – 8b = A. (3a + 4b)(3a + 4b + 2)。 B. (3a + 4b)(3a + 4b – 2)。 C. (3a + 4b)(3a – 4b + 2)。 D. (3a + 4b)(3a – 4b – 2)。

52. (3a + 4b)2 – 6a – 8b = (3a + 4b)2 – 2(3a + 4b) = (3a + 4b)(3a + 4b – 2) ∴ 答案是B。

53. pq – qr – 4p + 4r = A. (p + r)(q + 4)。 B. (p + r)(q – 4)。 C. (p – r)(q + 4)。 D. (p – r)(q – 4)。

53. pq – qr – 4p + 4r = q(p – r) – 4(p – r) = (p – r)(q – 4) ∴ 答案是D。

54. ab – ac + 2bc – 2b2 = A. (a + 2b)(b – c)。 B. (a + 2b)(c – b)。 C. (a – 2b)(b – c)。 D. (a – 2b)(c – b)。

54. ab – ac + 2bc – 2b2 = ab – 2b2 – ac + 2bc = b(a – 2b) – c(a – 2b) = (a – 2b)(b – c) ∴ 答案是C。

55. x2 – 5x + xy – xz – yz – 5y = A. (x + y)(x – z + 5)。 B. (x + y)(x – z – 5)。 C. (x – y)(x – z + 5)。 D. (x – y)(x – z – 5)。

55. x2 – 5x + xy – xz – yz – 5y = x2 – xz – 5x + xy – yz – 5y = x(x – z – 5) + y(x – z – 5) = (x + y)(x – z – 5) ∴ 答案是B。

56. 3(2m–5n)2 + (5n –2m)(5 –m)= 3(2m –5n)2–(2m –5n)(5–m) = (2m–5n)[3(2m–5n)–(5–m)]= (2m –5n)(6m –15n –5 +m) = (2m –5n)(7m –15n –5) ∴ 答案是D。

57. 下列哪些多項式彼此間有公因式？ I. a2 – bc + ab – ac II. b2 – ac + bc – ab III. c2 + ab – bc – ac A. 只有I及II B. 只有I及III C. 只有II及III D. I、II及III

58. 下列何者是 (x – 1)2 + 2(x – 1) + x(x + 1)的因式？ I. x – 1 II. x + 1 III. 2x – 1 A. 只有I及II B. 只有I及III C. 只有II及III D. I、II及III

58. (x – 1)2 + 2(x – 1) + x(x + 1) = (x – 1)[(x – 1) + 2] + x(x + 1) = (x – 1)(x + 1) + x(x + 1) = (x + 1)[(x – 1) + x]= (x + 1)(2x – 1) ∴ II及III是該多項式的因式。 ∴ 答案是C。

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49. 18x – 24y =
A. –6(3x – 4y)。
B. –6(3x + 4y)。
C. 6(3x – 4y)。
D. 6(3x + 4y)。

49. 18x – 24y
= 6(3x) – 6(4y)
= 6(3x – 4y)
∴ 答案是C。

50. –3e – 7de =
A. –e(3 – 7d)。
B. –e(3 + 7d)。
C. e(3 – 7d)。
D. e(3 + 7d)。

50. –3e – 7de
= –e(3) + (–e)(7d)
= –e(3 + 7d)
∴ 答案是B。

51. –12xy – 18xz + 24x² =
A. 6x(4x + 2y + 3z)。
B. 6x(4x + 2y – 3z)。
C. 6x(4x – 2y + 3z)。
D. 6x(4x – 2y – 3z)。

51. –12xy – 18xz + 24x²
= 6x(–2y – 3z + 4x)
= 6x(4x – 2y – 3z)
∴ 答案是D。

52. (3a + 4b)² – 6a – 8b =
A. (3a + 4b)(3a + 4b + 2)。
B. (3a + 4b)(3a + 4b – 2)。
C. (3a + 4b)(3a – 4b + 2)。
D. (3a + 4b)(3a – 4b – 2)。

52. (3a + 4b)² – 6a – 8b
= (3a + 4b)² – 2(3a + 4b)
= (3a + 4b)(3a + 4b – 2)
∴ 答案是B。

53. pq – qr – 4p + 4r =
A. (p + r)(q + 4)。
B. (p + r)(q – 4)。
C. (p – r)(q + 4)。
D. (p – r)(q – 4)。

53. pq – qr – 4p + 4r
= q(p – r) – 4(p – r)
= (p – r)(q – 4)
∴ 答案是D。

54. ab – ac + 2bc – 2b² =
A. (a + 2b)(b – c)。
B. (a + 2b)(c – b)。
C. (a – 2b)(b – c)。
D. (a – 2b)(c – b)。

54. ab – ac + 2bc – 2b²
= ab – 2b² – ac + 2bc
= b(a – 2b) – c(a – 2b)
= (a – 2b)(b – c)
∴ 答案是C。

55. x² – 5x + xy – xz – yz – 5y =
A. (x + y)(x – z + 5)。
B. (x + y)(x – z – 5)。
C. (x – y)(x – z + 5)。
D. (x – y)(x – z – 5)。

55. x² – 5x + xy – xz – yz – 5y
= x² – xz – 5x + xy – yz – 5y
= x(x – z – 5) + y(x – z – 5)
= (x + y)(x – z – 5)
∴ 答案是B。

56.
3(2m–5n)² + (5n –2m)(5 –m)
= 3(2m –5n)²–(2m –5n)(5–m)
= (2m–5n)[3(2m–5n)–(5–m)]
= (2m –5n)(6m –15n –5 +m)
= (2m –5n)(7m –15n –5)
∴ 答案是D。

57. 下列哪些多項式彼此間有公因式？
I. a² – bc + ab – ac
II. b² – ac + bc – ab
III. c² + ab – bc – ac
A. 只有I及II
B. 只有I及III
C. 只有II及III
D. I、II及III

58. 下列何者是 (x – 1)² + 2(x – 1) + x(x + 1)的因式？
I. x – 1
II. x + 1
III. 2x – 1
A. 只有I及II
B. 只有I及III
C. 只有II及III
D. I、II及III

58.
(x – 1)² + 2(x – 1) + x(x + 1)
= (x – 1)[(x – 1) + 2] + x(x + 1)
= (x – 1)(x + 1) + x(x + 1)
= (x + 1)[(x – 1) + x]
= (x + 1)(2x – 1)
∴ II及III是該多項式的因式。
∴ 答案是C。