ICSE Board Practice

Class VI Class VII Class VIII Class IX Class X
ICSE Grade X - Factor Theorem
Question 1
1.
Which of the following are true?
a)
If (x + a) is a factor of f(x), then f(a) = 0
b)
Zero of a polynomial and root of the polynomial are synonymous
c)
Zero of a polynomial is the value of the variable for which the polynomial value is zero
d)
A linear polynomial in one variable has only one root
e)
A polynomial of degree n has atmost n zeros
f)
Zero of a polynomial and zero polynomial are synonymous
g)
If (x - a) is a factor of f(x), then f(a) = 0
  • {a,b}
  • {b,c,d,e,g}
  • {a,f,d}
  • {f,c}
  • {a,e,g}
Question 2
2.
    • The quotient when
    • (
      −
      9
      d
      		)
    • is divided by
    • 4
    • is
  • (
    −
    11
    4
    d
    		)
  • (
    −
    7
    4
    d
    		)
  • (
    −
    5
    2
    d
    		)
  • (
    −
    9
    4
    d
    		)
  • (
    −
    13
    6
    d
    		)
Question 3
3.
    • Find the remainder when
    • (
      x
      2
       
      +
      15
      x
      +
      54
      		)
    • is divided by
    • (
      3
      x
      +
      5
      		)
  • 284
    9
  • 348
    11
  • 32
  • 286
    9
Question 4
4.
    • Given
    • f
      (
      t
      )
    • =
    • (
      −
      3
      t
      3
       
      −
      5
      t
      −
      8
      		)
    • ,
    • find
    •  
    • f
      (
      (-5)
      )
  • 394
  • 392
  • 391
  • 393
  • 390
Question 5
5.
    • In which of the cases,
    •  
    • g
      (
      x
      )
    •  
    • is a factor of
    •  
    • f
      (
      x
      )
    • ?
  • f
    (
    x
    )
    =
    (
    6
    x
    3
     
    +
    85
    x
    2
     
    +
    341
    x
    +
    360
    		)
    ,
    g
    (
    x
    )
    =
    (
    3
    x
    +
    7
    		)
  • f
    (
    x
    )
    =
    (
    6
    x
    3
     
    +
    89
    x
    2
     
    +
    391
    x
    +
    504
    		)
    ,
    g
    (
    x
    )
    =
    (
    −
    x
    +
    9
    		)
  • f
    (
    x
    )
    =
    (
    −
    3
    x
    3
     
    −
    4
    x
    2
     
    +
    223
    x
    +
    504
    		)
    ,
    g
    (
    x
    )
    =
    (
    −
    3
    x
    +
    5
    		)
  • f
    (
    x
    )
    =
    (
    −
    9
    x
    3
     
    −
    78
    x
    2
     
    −
    13
    x
    +
    280
    		)
    ,
    g
    (
    x
    )
    =
    (
    2
    x
    +
    9
    		)
  • f
    (
    x
    )
    =
    (
    −
    18
    x
    3
     
    −
    81
    x
    2
     
    +
    50
    x
    +
    225
    		)
    ,
    g
    (
    x
    )
    =
    (
    3
    x
    +
    5
    		)
Question 6
6.
    • Factorize
    • (
      x
      2
       
      +
      2
      x
      a
      +
      x
      +
      a
      2
       
      +
      a
      −
      72
      		)
      • (
        x
        +
        a
        +
        9
        		)
      • (
        x
        −
        a
        −
        8
        		)
      • (
        x
        +
        a
        +
        9
        		)
      • (
        x
        +
        a
        −
        8
        		)
      • (
        x
        −
        a
        −
        8
        		)
      • (
        x
        +
        a
        −
        9
        		)
      • (
        x
        +
        a
        −
        8
        		)
      • (
        x
        −
        a
        +
        9
        		)
      • (
        x
        −
        a
        +
        9
        		)
      • (
        x
        +
        a
        +
        8
        		)
Question 7
7.
    • (
      4
      x
      3
       
      y
      3
       
      +
      32
      x
      3
       
      y
      2
       
      		)
    • ÷
    		•
      2
      x
      2
       
      y
    • =
  • (
    2
    x
    2
     
    y
    4
     
    +
    16
    x
    y
    		)
  • (
    16
    x
    y
    2
     
    z
    +
    2
    x
    y
    2
     
    		)
  • (
    2
    x
    y
    2
     
    +
    16
    x
    y
    		)
  • (
    2
    x
    y
    2
     
    +
    16
    y
    2
     
    		)
  • (
    2
    x
    2
     
    y
    3
     
    +
    16
    x
    y
    		)
Question 8
8.
    • The remainder when
    • (
      2
      k
      4
       
      +
      8
      k
      2
       
      +
      k
      +
      8
      		)
    • is divided by
    • (
      k
      2
       
      +
      3
      k
      −
      40
      		)
    • is
  • (
    −
    557
    k
    +
    4248
    		)
  • (
    −
    556
    k
    +
    4248
    		)
  • (
    −
    560
    k
    +
    4248
    		)
  • (
    −
    558
    k
    +
    4248
    		)
  • (
    −
    554
    k
    +
    4248
    		)
Question 9
9.
    • If the polynomials
    •  
    • 6
      x
      2
      		  +  
      a
      x
      		  −  
      43
    •  
    • and
    • a
      x
      2
      		  −  
      x
      		  −  
      28
    • leave the same remainder when divided by
    • (
      x
      +
      3
      		)
    • ,
    • find the value of
    • a
  • 3
  • 6
  • 4
  • 0
  • 2
Question 10
10.
    • Given
    • f
      (
      n
      )
    • =
    • (
      −
      6
      n
      4
       
      −
      4
      n
      3
       
      −
      5
      n
      2
       
      −
      5
      n
      −
      3
      		)
    • ,
    • find
    •  
    • f
      (
      4
      )
  • -1892
  • -1896
  • -1894
  • -1895
  • -1897