ICSE Board Practice

Class VI Class VII Class VIII Class IX Class X
ICSE Grade X - Factor Theorem
Question 1
1.
    • Factorize
    • (
      2
      x
      3
       
      −
      26
      x
      +
      24
      		)
  • (
    x
    −
    1
    		)
    4
    (
    x
    −
    6
    		)
  • (
    x
    −
    1
    		)
    (
    x
    +
    4
    		)
    (
    2
    x
    −
    6
    		)
  • (
    x
    −
    1
    		)
    (
    2
    x
    +
    4
    		)
    (
    3
    x
    −
    6
    		)
  • (
    x
    −
    1
    		)
    (
    −
    2
    x
    +
    4
    		)
    (
    −
    6
    		)
  • (
    x
    −
    1
    		)
    (
    4
    x
    +
    4
    		)
    (
    5
    x
    −
    6
    		)
Question 2
2.
    • Find the remainder when
    • (
      3
      x
      2
       
      −
      17
      x
      +
      20
      		)
    • is divided by
    • (
      x
      −
      8
      		)
  • 75
  • 74
  • 78
  • 76
  • 77
Question 3
3.
    • Which of the following are true ?
a)
If the degree of p(x) is less then the degree of d(x), we should not divide p(x) with d(x)
b)
If p(x) is divided by (x - a), the remainder is p(a)
c)
Division of a polynomial with another polynomial stops when the degree of the remainder equals the degree of the divisor
d)
If p(a) = 0, then (x + a) perfectly divides p(x)
  • {a,b}
  • {c,b,a}
  • {d,b}
  • {c,d,a}
  • {c,a}
Question 4
4.
    • The remainder when
    • (
      −
      3
      e
      		)
    • is divided by
    • 6
    • is
  • 3
  • 1
  • 0
  • (
    −
    1
    		)
  • (
    −
    3
    		)
Question 5
5.
    • (
      28
      x
      3
       
      y
      3
       
      +
      4
      x
      3
       
      y
      2
       
      		)
    • ÷
    		•
      2
      x
      y
    • =
  • (
    2
    x
    2
     
    y
    2
     
    z
    +
    14
    x
    2
     
    y
    2
     
    		)
  • (
    14
    x
    3
     
    y
    4
     
    +
    2
    x
    2
     
    y
    		)
  • (
    14
    x
    2
     
    y
    2
     
    +
    2
    x
    2
     
    y
    		)
  • (
    14
    x
    3
     
    y
    3
     
    +
    2
    x
    2
     
    y
    		)
  • (
    14
    x
    2
     
    y
    2
     
    +
    2
    x
    y
    2
     
    		)
Question 6
6.
    • Factorize
    • (
      25
      x
      2
       
      +
      25
      x
      y
      +
      4
      y
      2
       
      		)
      • (
        5
        x
        +
        y
        		)
      • (
        5
        x
        −
        4
        y
        		)
      • (
        5
        x
        +
        y
        		)
      • (
        5
        x
        +
        4
        y
        		)
      • (
        5
        x
        −
        y
        		)
      • (
        5
        x
        +
        4
        y
        		)
      • (
        5
        x
        −
        y
        		)
      • (
        5
        x
        −
        4
        y
        		)
      • (
        5
        x
        +
        y
        		)
      • (
        5
        x
        −
        y
        		)
Question 7
7.
    • (
      −
      6
      x
      3
       
      +
      3
      x
      2
       
      +
      12
      x
      −
      9
      		)
    • ÷
    • (
      −
      6
      x
      2
       
      −
      3
      x
      +
      9
      		)
    • =
  • (
    −
    1
    		)
  • (
    −
    x
    −
    1
    		)
  • (
    2
    x
    −
    1
    		)
  • (
    x
    +
    1
    		)
  • (
    x
    −
    1
    		)
Question 8
8.
    • The quotient when
    • (
      −
      7
      r
      2
       
      		)
    • is divided by
    • (
      r
      +
      4
      		)
    • is
  • (
    −
    8
    r
    +
    28
    		)
  • (
    −
    5
    r
    +
    28
    		)
  • (
    −
    6
    r
    +
    28
    		)
  • (
    −
    10
    r
    +
    28
    		)
  • (
    −
    7
    r
    +
    28
    		)
Question 9
9.
    • The quotient when
    • (
      5
      a
      2
       
      +
      2
      a
      		)
    • is divided by
    • (
      a
      −
      8
      		)
    • is
  • (
    5
    a
    +
    42
    		)
  • (
    4
    a
    +
    42
    		)
  • (
    6
    a
    +
    42
    		)
  • (
    7
    a
    +
    42
    		)
  • (
    2
    a
    +
    42
    		)
Question 10
10.
    • The remainder when
    • (
      6
      q
      4
       
      −
      q
      3
       
      −
      7
      q
      2
       
      +
      7
      		)
    • is divided by
    • (
      q
      −
      7
      		)
    • is
  • 13728
  • 13727
  • 13730
  • 13726
  • 13724