EduSahara™ Assignment
Name : H.C.F and L.C.M of Polynomials
Chapter : Simplification of Algebraic Fractions
Grade : ICSE Grade VIII
License : Non Commercial Use
Question 1
1.
    • Find the H.C.F. of
    • 4
      x
    • and
    • 14
      x
      2
       
  • (i)
    2
    x
    2
     
  • (ii)
    2
    x
    3
     
  • (iii)
    2
    x
  • (iv)
    2
    x
    4
     
  • (v)
    28
    x
    2
     
Question 2
2.
    • Find the H.C.F. of
    • 24
      x
      y
    • and
    • 40
      x
      2
       
      y
      3
       
  • (i)
    8
    x
    2
     
    y
  • (ii)
    8
    x
    4
     
    y
  • (iii)
    120
    x
    2
     
    y
    3
     
  • (iv)
    8
    x
    y
    3
     
  • (v)
    8
    x
    y
Question 3
3.
    • Find the H.C.F. of
    • 18
      x
      2
       
      y
      3
       
      z
    • and
    • 30
      x
      y
      z
  • (i)
    90
    x
    2
     
    y
    3
     
    z
  • (ii)
    6
    x
    y
    3
     
    z
  • (iii)
    6
    x
    y
    z
  • (iv)
    6
    x
    2
     
    y
    z
  • (v)
    6
    x
    y
    z
    3
     
Question 4
4.
    • Find the L.C.M. of
    • 6
      x
      2
       
    • and
    • 54
      x
  • (i)
    324
    x
    3
     
  • (ii)
    6
    x
  • (iii)
    54
    x
    2
     
  • (iv)
    54
    x
    3
     
  • (v)
    54
    x
    4
     
Question 5
5.
    • Find the L.C.M. of
    • 2
      x
      2
       
      y
      3
       
    • and
    • 4
      x
      2
       
      y
  • (i)
    4
    x
    2
     
    y
    3
     
  • (ii)
    4
    x
    3
     
    y
    3
     
  • (iii)
    4
    x
    2
     
    y
    5
     
  • (iv)
    2
    x
    2
     
    y
  • (v)
    8
    x
    4
     
    y
    4
     
Question 6
6.
    • Find the L.C.M. of
    • 4
      x
      y
      z
    • and
    • 24
      x
      3
       
      y
      3
       
      z
      2
       
  • (i)
    24
    x
    4
     
    y
    3
     
    z
    2
     
  • (ii)
    24
    x
    3
     
    y
    3
     
    z
    2
     
  • (iii)
    96
    x
    4
     
    y
    4
     
    z
    3
     
  • (iv)
    24
    x
    3
     
    y
    5
     
    z
    2
     
  • (v)
    4
    x
    y
    z
Question 7
7.
    • Find the H.C.F. of
    • (
      x
      2
       
      −
      16
      x
      +
      63
      		)
    • and
    • (
      x
      2
       
      −
      4
      x
      −
      21
      		)
  • (i)
    (
    x
    +
    3
    		)
  • (ii)
    (
    x
    −
    9
    		)
  • (iii)
    (
    2
    x
    −
    7
    		)
  • (iv)
    (
    2
    x
    −
    9
    		)
  • (v)
    (
    x
    −
    7
    		)
Question 8
8.
    • Find the L.C.M. of
    • (
      x
      2
       
      +
      4
      x
      −
      5
      		)
    • ,
    • (
      x
      2
       
      +
      x
      −
      2
      		)
    • and
    • (
      x
      2
       
      +
      7
      x
      +
      10
      		)
  • (i)
      • (
        x
        −
        1
        		)
      • (
        x
        +
        2
        		)
      • (
        x
        +
        8
        		)
  • (ii)
      • (
        x
        +
        5
        		)
      • (
        x
        −
        1
        		)
      • (
        x
        +
        2
        		)
  • (iii)
      • (
        x
        +
        5
        		)
      • (
        x
        −
        1
        		)
      • (
        x
        +
        8
        		)
  • (iv)
      • (
        x
        +
        5
        		)
      • (
        x
        −
        1
        		)
      • (
        x
        −
        7
        		)
  • (v)
      • (
        x
        +
        5
        		)
      • (
        x
        +
        2
        		)
      • (
        x
        +
        8
        		)
Question 9
9.
    • Find the L.C.M. of
    • (
      8
      x
      2
       
      +
      14
      x
      y
      +
      5
      y
      2
       
      		)
    • and
    • (
      32
      x
      2
       
      +
      52
      x
      y
      +
      15
      y
      2
       
      		)
  • (i)
      • (
        2
        x
        +
        y
        		)
      • (
        4
        x
        +
        5
        y
        		)
      • (
        5
        x
        +
        7
        y
        		)
  • (ii)
      • (
        8
        x
        +
        3
        y
        		)
      • (
        2
        x
        +
        y
        		)
      • (
        5
        x
        +
        7
        y
        		)
  • (iii)
      • (
        2
        x
        +
        y
        		)
      • (
        4
        x
        +
        5
        y
        		)
      • (
        8
        x
        +
        3
        y
        		)
  • (iv)
      • (
        4
        x
        +
        5
        y
        		)
      • (
        8
        x
        +
        3
        y
        		)
      • (
        5
        x
        +
        7
        y
        		)
  • (v)
      • (
        2
        x
        +
        y
        		)
      • (
        4
        x
        +
        5
        y
        		)
      • (
        5
        x
        +
        y
        		)
Question 10
10.
Which of the following gives the L.C.M. of two or more polynomials?
  • (i)
    ( Product of numerical coefficients ) ✕ ( Each common factor raised to the lowest power )
  • (ii)
    ( L.C.M. of numerical coefficients ) ✕ ( Each common factor raised to the highest power )
  • (iii)
    ( Product of numerical coefficients ) ✕ ( Each common factor raised to the highest power )
  • (iv)
    ( L.C.M. of numerical coefficients ) ✕ ( Each common factor raised to the lowest power )
Question 11
11.
Which of the following gives the H.C.F of two or more polynomials?
  • (i)
    ( H.C.F. of numerical coefficients ) ✕ ( Each common factor raised to the highest power )
  • (ii)
    ( H.C.F. of numerical coefficients ) ✕ ( Each common factor raised to the lowest power )
  • (iii)
    ( Product of numerical coefficients ) ✕ ( Each common factor raised to the lowest power )
  • (iv)
    ( Product of numerical coefficients ) ✕ ( Each common factor raised to the highest power )
    Assignment Key
  •  1) (iii)
  •  2) (v)
  •  3) (iii)
  •  4) (iii)
  •  5) (i)
  •  6) (ii)
  •  7) (v)
  •  8) (ii)
  •  9) (iii)
  •  10) (ii)
  •  11) (ii)