EduSahara™ Assignment
Name : Factorisation Miscellaneous
Chapter : Factorisation
Grade : SSC Grade VIII
License : Non Commercial Use
Question 1
1.
    • Find the prime factorization of
    • 4
  • (i)
    2 2
     
  • (ii)
    5 2
     
  • (iii)
    (-1) 2
     
  • (iv)
    2
  • (v)
    2 3
     
Question 2
2.
    • Find the prime factorization of
    • 65
  • (i)
    5
    		✕
    13 2
     
  • (ii)
    4
    		✕
    13
  • (iii)
    5
    		✕
    15
  • (iv)
    2
    		✕
    13
  • (v)
    5
    		✕
    13
Question 3
3.
    • Which of the following is a factor of
    • 15
      x
      5
       
      y
      2
       
      z
    • ?
  • (i)
    x
    6
     
    y
  • (ii)
    y
  • (iii)
    y
    z
    2
     
  • (iv)
    y
    3
     
  • (v)
    x
    5
     
    y
    z
    2
     
Question 4
4.
    • Which of the following is not a factor of
    • 45
      x
      3
       
      y
      5
       
      z
      4
       
    • ?
  • (i)
    45
    x
    3
     
    y
    4
     
    z
    4
     
  • (ii)
    45
    x
    y
    4
     
    z
  • (iii)
    45
    x
    2
     
    y
    5
     
    z
    4
     
  • (iv)
    45
    x
    3
     
    y
    5
     
    z
    3
     
  • (v)
    45
    x
    3
     
    y
    6
     
    z
    5
     
Question 5
5.
    • Which of the following is a factor of
    • (
      x
      2
       
      +
      y
      5
       
      z
      3
       
      		)
    • ?
  • (i)
    y
  • (ii)
    no factors
  • (iii)
    y
    5
     
    z
    3
     
  • (iv)
    x
    z
  • (v)
    x
    2
     
Question 6
6.
    • Which of the following is an irreducible factor of
    • 2
      x
      5
       
      y
      5
       
      z
      2
       
    • ?
  • (i)
    y
    3
     
    z
  • (ii)
    x
  • (iii)
    x
    2
     
    y
  • (iv)
    x
    z
    2
     
  • (v)
    x
    2
     
    y
    3
     
    z
    2
     
Question 7
7.
    • Which of the following is not an irreducible factor of
    • (
      x
      2
       
      y
      +
      x
      y
      2
       
      +
      x
      y
      		)
    • ?
  • (i)
    x
    y
  • (ii)
    x
  • (iii)
    y
  • (iv)
    (
    x
    +
    y
    +
    1
    		)
Question 8
8.
    • Which of the following are true ?
a)
Division of a polynomial with another polynomial stops when the degree of the remainder equals the degree of the divisor
b)
If p(a) = 0, then (x + a) perfectly divides p(x)
c)
If p(x) is divided by (x - a), the remainder is p(a)
d)
If the degree of p(x) is less then the degree of d(x), we should not divide p(x) with d(x)
  • (i)
    {a,d,c}
  • (ii)
    {a,c}
  • (iii)
    {c,d}
  • (iv)
    {a,b,c}
  • (v)
    {b,d}
Question 9
9.
    • In which of the cases,
    •  
    • g
      (
      x
      )
    •  
    • is a factor of
    •  
    • f
      (
      x
      )
    • ?
  • (i)
    f
    (
    x
    )
    =
    (
    2
    x
    3
     
    +
    x
    2
     
    −
    25
    x
    +
    12
    		)
    ,
    g
    (
    x
    )
    =
    (
    x
    +
    4
    		)
  • (ii)
    f
    (
    x
    )
    =
    (
    2
    x
    3
     
    −
    21
    x
    2
     
    +
    22
    x
    +
    144
    		)
    ,
    g
    (
    x
    )
    =
    (
    −
    2
    x
    +
    1
    		)
  • (iii)
    f
    (
    x
    )
    =
    (
    4
    x
    3
     
    −
    12
    x
    2
     
    −
    31
    x
    +
    18
    		)
    ,
    g
    (
    x
    )
    =
    (
    −
    x
    +
    3
    		)
  • (iv)
    f
    (
    x
    )
    =
    (
    −
    x
    3
     
    −
    3
    x
    2
     
    +
    10
    x
    +
    24
    		)
    ,
    g
    (
    x
    )
    =
    (
    −
    2
    x
    +
    9
    		)
  • (v)
    f
    (
    x
    )
    =
    (
    2
    x
    3
     
    −
    11
    x
    2
     
    −
    3
    x
    +
    54
    		)
    ,
    g
    (
    x
    )
    =
    (
    −
    x
    +
    8
    		)
Question 10
10.
    • (
      16
      x
      4
       
      +
      16
      x
      3
       
      		)
    • ÷
    • 4
      x
      2
       
  • (i)
    (
    3
    x
    2
     
    +
    4
    x
    		)
  • (ii)
    (
    4
    x
    2
     
    −
    4
    x
    		)
  • (iii)
    (
    −
    4
    x
    2
     
    +
    4
    x
    		)
  • (iv)
    (
    4
    x
    2
     
    +
    5
    x
    		)
  • (v)
    (
    4
    x
    2
     
    +
    4
    x
    		)
Question 11
11.
    • (
      2
      x
      4
       
      +
      10
      x
      3
       
      +
      12
      x
      2
       
      		)
    • ÷
    • (
      2
      x
      2
       
      +
      4
      x
      		)
  • (i)
    3
    x
  • (ii)
    (
    −
    x
    2
     
    +
    3
    x
    		)
  • (iii)
    (
    x
    2
     
    −
    3
    x
    		)
  • (iv)
    (
    x
    2
     
    +
    4
    x
    		)
  • (v)
    (
    x
    2
     
    +
    3
    x
    		)
Question 12
12.
    • (
      6
      x
      4
       
      −
      54
      x
      3
       
      −
      24
      x
      2
       
      +
      216
      x
      		)
    • ÷
    • (
      3
      x
      2
       
      −
      33
      x
      +
      54
      		)
  • (i)
    (
    −
    2
    x
    2
     
    +
    4
    x
    		)
  • (ii)
    (
    2
    x
    2
     
    +
    4
    x
    		)
  • (iii)
    (
    2
    x
    2
     
    +
    5
    x
    		)
  • (iv)
    (
    2
    x
    2
     
    −
    4
    x
    		)
  • (v)
    (
    2
    x
    2
     
    +
    3
    x
    		)
    Assignment Key
  •  1) (i)
  •  2) (v)
  •  3) (ii)
  •  4) (v)
  •  5) (ii)
  •  6) (ii)
  •  7) (i)
  •  8) (iii)
  •  9) (i)
  •  10) (v)
  •  11) (v)
  •  12) (ii)