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Home › Grade8 › OLYMPIAD › Math Olympiad-Grade-8 › Algebraic Expressions › Factorisation Worksheet-2

Factorisation Worksheet-2

Factorisation Worksheet-2

 

  1. If the factors of a2 + b2 + 2(ab + bc + ca) are (a + b + m) and (a + b + nc), then the value of m + n is:

(a) 0                    (b) 2                    (c) 4                    (d) 6

 

  1. If (x2 + 3x + 5) (x2 – 3x + 5) = n2 – n2, then m = ______.

(a) x2 – 3x         (b) 3x                  (c) x2 + 5            (d) None of these

 

  1. One of the factors of (a2 – b2) (c2 – d2) – 4abcd is:

(a) (ac – bd + bc + ad)                (b) ac – bd + bc – ad

(c) cannot be determined           (d) none of these

 

  1. The factors of are:

(a)                  (b)

(c)                  (d)

 

  1. One of the factors of x7 + xy6 is:

(a) x2 + y2                                       (b) x

(c) either A or B                            (d) neither A nor B

 

  1. Factors of a2 + 4a + 4 are:

(a) (a + 2)2        (b) (a + 1)2         (c) (a – 2)2        (d) (a – 1)2

 

  1. x3 + 6x2 + 9x can be factorised as:

(a) x2(x + 2)2    (b) x(x + 3)2      (c) x(x + 3)        (d) None of these

 

  1. (2x + 3y)2 + 2(2x + 3y) (x + y) + (x + y)2 can be factorised as:

(a) (3x + 4y) (3x – 4y)                (b) (3x + 4y)2

(c) (3x + 2y) (2x – 3y)                (d) None of these

 

  1. Factors for a2b2 + c2d2 – a2c2 – b2d2 are:

(a) (a + d) (a – d) (b + c) (b – c)

(b) (a2 – b2)

(c) (a2 – d2) (b2 – c2)

(d) None of these

 

  1. Factors of 8x3 + 27y3 are:

(a) (x + 2) (x2 – 2x + 4)

(b) (3x + 4) (ax2 – 12x + 16)

(c) (2x + 3y) (4x2 – 6xy + 9y2)

(d) (x – 1) (x2 + 4x + 7)

 

  1. a12 – 1 can be factorised as:

(a) (a – 1) (a – 2) (a – 3) (a – 4)

(b) (a – 1) (a2 + a + 1) (a + 1) (a2 + a + 1)

(c) (a2 + a + 1) (a2 – a + 1)

(d) (a – 1) (a2 + a + 1) (a + 1) (a2 – a + 1) [(a2 + 1) (a4 – a2 + 1)]

 

  1. If x + y + z = 0, then x3 + y3 + z3 = ______.

(a) 3xyz              (b) x2yz               (c) xy2z               (d) xyz2

 

  1. Factorization of (a – b)3 + (b – c)3 + (c – a)3 is:

(a) (a – b) (a – c)                         (b) (a – b) (b – c) (c – a)

(c) 3(a – b) (b – c) (c – a)          (d) 32(a – b) (b – c) (c – a)

 

  1. The factors of x2 + 7x + 12 are:

(a) (x + 2) (x + 1)                          (b) (x + 3) (x + 2)

(c) (x + 4) (x + 3)                         (d) None of these

 

  1. Factors of x2 – 3x – 18 are:

(a) (x – 6) (x + 3)                         (b) (x – 6) (x – 3)

(c) (x – 3)2                                     (d) (x + 6)2

 

Answer Key:

(1)-b; (2)-c; (3)-a; (4)-d; (5)-c; (6)-a; (7)-b; (8)-b; (9)-a; (10)-c; (11)-d; (12)-a; (13)-c; (14)-c; (15)-a