EduSahara™ Assignment
Name : Remainder Theorem
Chapter : Polynomials and Factorisation
Grade : SSC Grade IX
License : Non Commercial Use
Question 1
1.
    • The quotient when
    • 2
      e
      2
       
    • is divided by
    • (
      e
      −
      1
      		)
    • is
  • (i)
    (
    3
    e
    +
    2
    		)
  • (ii)
    (
    e
    +
    2
    		)
  • (iii)
    2
  • (iv)
    (
    2
    e
    +
    2
    		)
  • (v)
    (
    4
    e
    +
    2
    		)
Question 2
2.
    • The quotient when
    • (
      5
      h
      −
      6
      		)
    • is divided by
    • (
      h
      +
      1
      		)
    • is
  • (i)
    4
  • (ii)
    5
  • (iii)
    3
  • (iv)
    6
  • (v)
    7
Question 3
3.
    • The quotient when
    • (
      −
      4
      r
      2
       
      +
      4
      r
      −
      6
      		)
    • is divided by
    • (
      r
      +
      8
      		)
    • is
  • (i)
    (
    −
    2
    r
    +
    36
    		)
  • (ii)
    (
    −
    6
    r
    +
    36
    		)
  • (iii)
    (
    −
    4
    r
    +
    36
    		)
  • (iv)
    (
    −
    3
    r
    +
    36
    		)
  • (v)
    (
    −
    5
    r
    +
    36
    		)
Question 4
4.
    • The quotient when
    • (
      −
      2
      w
      2
       
      −
      2
      w
      		)
    • is divided by
    • (
      w
      −
      9
      		)
    • is
  • (i)
    (
    −
    w
    −
    20
    		)
  • (ii)
    (
    w
    −
    20
    		)
  • (iii)
    (
    −
    3
    w
    −
    20
    		)
  • (iv)
    (
    −
    2
    w
    −
    20
    		)
  • (v)
    (
    −
    5
    w
    −
    20
    		)
Question 5
5.
    • The quotient when
    • (
      −
      3
      t
      5
       
      −
      5
      t
      4
       
      +
      8
      t
      3
       
      −
      7
      t
      2
       
      −
      7
      t
      +
      9
      		)
    • is divided by
    • (
      t
      +
      3
      		)
    • is
  • (i)
    (
    −
    4
    t
    4
     
    +
    4
    t
    3
     
    −
    4
    t
    2
     
    +
    5
    t
    −
    22
    		)
  • (ii)
    (
    −
    2
    t
    4
     
    +
    4
    t
    3
     
    −
    4
    t
    2
     
    +
    5
    t
    −
    22
    		)
  • (iii)
    (
    −
    3
    t
    4
     
    +
    4
    t
    3
     
    −
    4
    t
    2
     
    +
    5
    t
    −
    22
    		)
  • (iv)
    (
    −
    5
    t
    4
     
    +
    4
    t
    3
     
    −
    4
    t
    2
     
    +
    5
    t
    −
    22
    		)
  • (v)
    (
    −
    t
    4
     
    +
    4
    t
    3
     
    −
    4
    t
    2
     
    +
    5
    t
    −
    22
    		)
Question 6
6.
    • The remainder when
    • (
      −
      u
      		)
    • is divided by
    • 6
    • is
  • (i)
    1
  • (ii)
    0
  • (iii)
    (
    −
    3
    		)
  • (iv)
    (
    −
    1
    		)
  • (v)
    3
Question 7
7.
    • The remainder when
    • (
      −
      t
      2
       
      		)
    • is divided by
    • (
      t
      +
      4
      		)
    • is
  • (i)
    (
    −
    15
    		)
  • (ii)
    (
    −
    19
    		)
  • (iii)
    (
    −
    13
    		)
  • (iv)
    (
    −
    16
    		)
  • (v)
    (
    −
    17
    		)
Question 8
8.
    • The remainder when
    • (
      4
      y
      −
      2
      		)
    • is divided by
    • (
      y
      −
      3
      		)
    • is
  • (i)
    12
  • (ii)
    10
  • (iii)
    11
  • (iv)
    8
  • (v)
    9
Question 9
9.
    • The remainder when
    • (
      3
      k
      2
       
      −
      2
      k
      		)
    • is divided by
    • (
      k
      +
      8
      		)
    • is
  • (i)
    205
  • (ii)
    208
  • (iii)
    209
  • (iv)
    211
  • (v)
    207
Question 10
10.
    • The remainder when
    • (
      −
      5
      p
      2
       
      −
      6
      p
      −
      3
      		)
    • is divided by
    • (
      p
      −
      3
      		)
    • is
  • (i)
    (
    −
    66
    		)
  • (ii)
    (
    −
    67
    		)
  • (iii)
    (
    −
    68
    		)
  • (iv)
    (
    −
    64
    		)
  • (v)
    (
    −
    65
    		)
Question 11
11.
    • Find the remainder when
    • (
      2
      x
      2
       
      −
      21
      x
      +
      49
      		)
    • is divided by
    • (
      x
      −
      1
      		)
  • (i)
    29
  • (ii)
    30
  • (iii)
    27
  • (iv)
    33
  • (v)
    31
Question 12
12.
    • If
    • f
      (
      x
      )
    • =
    • (
      4
      x
      3
       
      +
      14
      x
      2
       
      −
      20
      x
      −
      48
      		)
    • and
    • g
      (
      x
      )
    • =
    • (
      6
      x
      3
       
      +
      26
      x
      2
       
      −
      12
      x
      −
      80
      		)
    • have a common factor, find the common factor
  • (i)
    (
    x
    +
    4
    		)
  • (ii)
    (
    2
    x
    +
    4
    		)
  • (iii)
    (
    3
    x
    −
    5
    		)
  • (iv)
    (
    2
    x
    +
    3
    		)
  • (v)
    (
    2
    x
    −
    4
    		)
Question 13
13.
    • If the polynomial
    •  
    • b
      x
      2
      		  +  
      a
    •  
    • is divided by
    • (
      x
      −
      5
      		)
    • ,
    • it leaves a remainder
    • 21
    • .
    • If it is divided by
    • (
      2
      x
      −
      1
      		)
    • ,
    • it leaves a remainder
    • (
      -3
      3
      4
      		 )
    • .
    • Find the value of
    • a
    • and
    • b
  • (i)
      • 0
      • ,
      • -5
  • (ii)
      • -4
      • ,
      • 2
  • (iii)
      • -3
      • ,
      • 1
  • (iv)
      • -4
      • ,
      • 1
  • (v)
      • 2
      • ,
      • -3
    Assignment Key
  •  1) (iv)
  •  2) (ii)
  •  3) (iii)
  •  4) (iv)
  •  5) (iii)
  •  6) (ii)
  •  7) (iv)
  •  8) (ii)
  •  9) (ii)
  •  10) (i)
  •  11) (ii)
  •  12) (i)
  •  13) (iv)