EduSahara™ Assignment
Name : Remainder Theorem
Chapter : Polynomials and Factorisation
Grade : SSC Grade IX
License : Non Commercial Use
Question 1
1.
    • The quotient when
    • g
      2
       
    • is divided by
    • (
      g
      −
      9
      		)
    • is
  • (i)
    (
    2
    g
    +
    9
    		)
  • (ii)
    (
    −
    g
    +
    9
    		)
  • (iii)
    9
  • (iv)
    (
    g
    +
    9
    		)
  • (v)
    (
    4
    g
    +
    9
    		)
Question 2
2.
    • The quotient when
    • (
      −
      5
      y
      −
      5
      		)
    • is divided by
    • (
      y
      −
      1
      		)
    • is
  • (i)
    (
    −
    7
    		)
  • (ii)
    (
    −
    2
    		)
  • (iii)
    (
    −
    4
    		)
  • (iv)
    (
    −
    6
    		)
  • (v)
    (
    −
    5
    		)
Question 3
3.
    • The quotient when
    • (
      −
      7
      w
      2
       
      +
      5
      w
      −
      1
      		)
    • is divided by
    • (
      w
      +
      7
      		)
    • is
  • (i)
    (
    −
    8
    w
    +
    54
    		)
  • (ii)
    (
    −
    7
    w
    +
    54
    		)
  • (iii)
    (
    −
    9
    w
    +
    54
    		)
  • (iv)
    (
    −
    6
    w
    +
    54
    		)
  • (v)
    (
    −
    4
    w
    +
    54
    		)
Question 4
4.
    • The quotient when
    • (
      4
      p
      2
       
      −
      4
      p
      		)
    • is divided by
    • (
      p
      +
      8
      		)
    • is
  • (i)
    (
    6
    p
    −
    36
    		)
  • (ii)
    (
    4
    p
    −
    36
    		)
  • (iii)
    (
    3
    p
    −
    36
    		)
  • (iv)
    (
    2
    p
    −
    36
    		)
  • (v)
    (
    5
    p
    −
    36
    		)
Question 5
5.
    • The quotient when
    • (
      −
      8
      z
      5
       
      +
      z
      4
       
      −
      4
      z
      3
       
      +
      7
      z
      2
       
      −
      4
      z
      +
      3
      		)
    • is divided by
    • (
      z
      +
      2
      		)
    • is
  • (i)
    (
    −
    9
    z
    4
     
    +
    17
    z
    3
     
    −
    38
    z
    2
     
    +
    83
    z
    −
    170
    		)
  • (ii)
    (
    −
    5
    z
    4
     
    +
    17
    z
    3
     
    −
    38
    z
    2
     
    +
    83
    z
    −
    170
    		)
  • (iii)
    (
    −
    7
    z
    4
     
    +
    17
    z
    3
     
    −
    38
    z
    2
     
    +
    83
    z
    −
    170
    		)
  • (iv)
    (
    −
    11
    z
    4
     
    +
    17
    z
    3
     
    −
    38
    z
    2
     
    +
    83
    z
    −
    170
    		)
  • (v)
    (
    −
    8
    z
    4
     
    +
    17
    z
    3
     
    −
    38
    z
    2
     
    +
    83
    z
    −
    170
    		)
Question 6
6.
    • The remainder when
    • (
      −
      8
      n
      		)
    • is divided by
    • 5
    • is
  • (i)
    3
  • (ii)
    (
    −
    3
    		)
  • (iii)
    0
  • (iv)
    1
  • (v)
    (
    −
    1
    		)
Question 7
7.
    • The remainder when
    • 6
      f
      2
       
    • is divided by
    • (
      f
      +
      8
      		)
    • is
  • (i)
    387
  • (ii)
    383
  • (iii)
    384
  • (iv)
    381
  • (v)
    385
Question 8
8.
    • The remainder when
    • (
      2
      d
      −
      4
      		)
    • is divided by
    • (
      d
      +
      5
      		)
    • is
  • (i)
    (
    −
    16
    		)
  • (ii)
    (
    −
    14
    		)
  • (iii)
    (
    −
    15
    		)
  • (iv)
    (
    −
    13
    		)
  • (v)
    (
    −
    11
    		)
Question 9
9.
    • The remainder when
    • (
      3
      e
      2
       
      −
      2
      e
      		)
    • is divided by
    • (
      e
      +
      7
      		)
    • is
  • (i)
    160
  • (ii)
    161
  • (iii)
    164
  • (iv)
    162
  • (v)
    159
Question 10
10.
    • The remainder when
    • (
      5
      a
      2
       
      +
      9
      a
      −
      2
      		)
    • is divided by
    • (
      a
      +
      6
      		)
    • is
  • (i)
    123
  • (ii)
    124
  • (iii)
    121
  • (iv)
    127
  • (v)
    125
Question 11
11.
    • Find the remainder when
    • (
      9
      x
      2
       
      +
      30
      x
      +
      21
      		)
    • is divided by
    • (
      x
      +
      3
      		)
  • (i)
    15
  • (ii)
    11
  • (iii)
    10
  • (iv)
    13
  • (v)
    12
Question 12
12.
    • If
    • f
      (
      x
      )
    • =
    • (
      6
      x
      3
       
      +
      18
      x
      2
       
      −
      24
      		)
    • and
    • g
      (
      x
      )
    • =
    • (
      18
      x
      3
       
      +
      3
      x
      2
       
      −
      15
      x
      −
      6
      		)
    • have a common factor, find the common factor
  • (i)
    (
    3
    x
    +
    2
    		)
  • (ii)
    (
    2
    x
    +
    4
    		)
  • (iii)
    (
    3
    x
    −
    3
    		)
  • (iv)
    (
    x
    +
    2
    		)
  • (v)
    (
    2
    x
    +
    1
    		)
Question 13
13.
    • If the polynomial
    •  
    • 4
      x
      2
      		  +  
      a
      x
      		  +  
      b
    •  
    • is divided by
    • (
      3
      x
      −
      4
      		)
    • ,
    • it leaves a remainder
    • 51
      1
      9
    • .
    • If it is divided by
    • (
      2
      x
      +
      1
      		)
    • ,
    • it leaves a remainder
    • 12
    • .
    • Find the value of
    • a
    • and
    • b
  • (i)
      • 19
      • ,
      • 17
  • (ii)
      • 21
      • ,
      • 19
  • (iii)
      • 18
      • ,
      • 21
  • (iv)
      • 19
      • ,
      • 20
  • (v)
      • 18
      • ,
      • 20
    Assignment Key
  •  1) (iv)
  •  2) (v)
  •  3) (ii)
  •  4) (ii)
  •  5) (v)
  •  6) (iii)
  •  7) (iii)
  •  8) (ii)
  •  9) (ii)
  •  10) (ii)
  •  11) (v)
  •  12) (iii)
  •  13) (v)