ICSE Board Practice

Class VI Class VII Class VIII Class IX Class X
ICSE Grade X - Factor Theorem
Question 1
1.
    • The quotient when
    • 6
      a
      2
       
    • is divided by
    • (
      a
      −
      4
      		)
    • is
  • (
    4
    a
    +
    24
    		)
  • (
    7
    a
    +
    24
    		)
  • (
    6
    a
    +
    24
    		)
  • (
    5
    a
    +
    24
    		)
  • (
    9
    a
    +
    24
    		)
Question 2
2.
    • If
    • (
      x
      2
       
      −
      1
      		)
    • is a factor of
    •  
    • a
      x
      4
      		  +  
      b
      x
      3
      		  +  
      c
      x
      2
      		  +  
      d
      x
      		  +  
      e
    • ,
    • which of the following are true ?
a)
a + b + c = d + e
b)
d + e = 0
c)
a + b + c = 0
d)
a + b + c + d + e = 0
e)
a + c + e = 0
f)
b + d = 0
  • {a,d}
  • {b,d,e}
  • {b,e}
  • {d,e,f}
  • {c,a,f}
Question 3
3.
    • The value of the polynomial
    • (
      2
      r
      +
      3
      		)
    • at
    •  
    • r
    • =
    • 3
    • is
  • 8
  • 6
  • 10
  • 12
  • 9
Question 4
4.
    • The remainder when
    • (
      −
      9
      m
      2
       
      +
      m
      +
      8
      		)
    • is divided by
    • (
      m
      +
      6
      		)
    • is
  • (
    −
    324
    		)
  • (
    −
    321
    		)
  • (
    −
    320
    		)
  • (
    −
    322
    		)
  • (
    −
    323
    		)
Question 5
5.
    • The degree of the polynomial
    • (
      −
      3
      i
      −
      7
      		)
    • is
  • 3
  • 0
  • 1
  • 2
  • (-2)
Question 6
6.
    • Which of the following are possible values
    • for the length and breadth of a rectangle
    • whose area is
    • (
      −
      6
      x
      2
       
      −
      23
      x
      −
      20
      		)
      • (
        x
        −
        4
        		)
      • (
        −
        3
        x
        +
        4
        		)
      • (
        2
        x
        −
        5
        		)
      • (
        −
        3
        x
        +
        4
        		)
      • (
        2
        x
        +
        5
        		)
      • (
        −
        3
        x
        +
        4
        		)
      • (
        2
        x
        −
        5
        		)
      • (
        −
        3
        x
        −
        4
        		)
      • (
        2
        x
        +
        5
        		)
      • (
        −
        3
        x
        −
        4
        		)
Question 7
7.
    • (
      12
      x
      4
       
      +
      20
      x
      3
       
      		)
    • ÷
    • 4
      x
      2
       
  • (
    −
    3
    x
    2
     
    +
    5
    x
    		)
  • (
    3
    x
    2
     
    −
    5
    x
    		)
  • (
    2
    x
    2
     
    +
    5
    x
    		)
  • (
    3
    x
    2
     
    +
    5
    x
    		)
  • (
    3
    x
    2
     
    +
    6
    x
    		)
Question 8
8.
    • Factorize
    • (
      2
      x
      2
       
      +
      3
      x
      −
      27
      		)
  • (
    x
    −
    3
    		)
    (
    3
    x
    +
    9
    		)
  • (
    x
    −
    3
    		)
    (
    2
    x
    +
    9
    		)
  • (
    x
    −
    3
    		)
    (
    −
    x
    +
    9
    		)
  • (
    x
    −
    3
    		)
    (
    4
    x
    +
    9
    		)
  • (
    x
    −
    3
    		)
    (
    x
    +
    9
    		)
Question 9
9.
    • If one of the roots of the cubic equation
    • (
      x
      3
       
      −
      31
      x
      +
      30
      		)
      =
      0
    • is
    • (
      −
      6
      )
    • ,
    • find the remaining real roots
  • (
    (
    −
    8
    )
    ,
    (
    −
    1
    )
    )
  • (
    (
    −
    7
    )
    ,
    0
    )
  • (
    (
    −
    3
    )
    ,
    3
    )
  • (
    1
    ,
    5
    )
  • (
    (
    −
    5
    )
    ,
    2
    )
Question 10
10.
    • The value of the polynomial
    • (
      4
      t
      4
       
      +
      t
      3
       
      +
      5
      t
      2
       
      −
      t
      −
      1
      		)
    • at
    •  
    • t
    • =
    • 5
    • is
  • 2744
  • 2743
  • 2745
  • 2747
  • 2742