CBSE Board Practice

Class VI Class VII Class VIII Class IX Class X
CBSE Grade IX - Polynomials
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 zero polynomial are synonymous
c)
Zero of a polynomial and root of the polynomial are synonymous
d)
If (x - a) is a factor of f(x), then f(a) = 0
e)
A linear polynomial in one variable has only one root
f)
Zero of a polynomial is the value of the variable for which the polynomial value is zero
g)
A polynomial of degree n has atmost n zeros
  • {a,c}
  • {c,d,e,f,g}
  • {a,f,g}
  • {a,b,e}
  • {b,d}
Question 2
2.
Which of the following algebraic expressions is a constant polynomial?
  • (
    7
    u
    3
     
    +
    6
    u
    2
     
    +
    6
    u
    −
    1
    		)
  • (
    u
    −
    9
    		)
  • (
    9
    u
    5
     
    −
    8
    u
    4
     
    −
    6
    u
    2
     
    +
    3
    u
    +
    8
    		)
  • 2
  • (
    8
    u
    2
     
    +
    2
    u
    −
    6
    		)
Question 3
3.
    • Factorize
    • (
      9
      a
      2
       
      −
      6
      a
      b
      +
      b
      2
       
      		)
  • (
    −
    4
    a
    +
    b
    		)
    (
    −
    4
    a
    +
    b
    		)
  • (
    −
    2
    a
    +
    b
    		)
    (
    −
    2
    a
    +
    b
    		)
  • (
    −
    3
    a
    −
    2
    b
    		)
    (
    −
    3
    a
    −
    b
    		)
  • (
    −
    3
    a
    +
    b
    		)
    (
    −
    3
    a
    +
    b
    		)
  • (
    −
    3
    a
    +
    4
    b
    		)
    (
    −
    3
    a
    +
    3
    b
    		)
Question 4
4.
    • If the polynomials
    •  
    • 6
      x
      2
      		  +  
      a
      x
      		  −  
      74
    •  
    • and
    • a
      x
      2
      		  +  
      4
      x
      		  +  
      40
    • leave the same remainder when divided by
    • (
      x
      +
      3
      		)
    • ,
    • find the value of
    • a
  • (-4)
  • (-3)
  • (-5)
  • (-2)
  • (-6)
Question 5
5.
    • (
      −
      24
      x
      4
       
      −
      56
      x
      3
       
      +
      2
      x
      2
       
      +
      60
      x
      +
      18
      		)
    • ÷
    • (
      8
      x
      3
       
      +
      16
      x
      2
       
      −
      6
      x
      −
      18
      		)
    • =
  • (
    −
    2
    x
    −
    1
    		)
  • (
    −
    4
    x
    −
    1
    		)
  • (
    3
    x
    −
    1
    		)
  • (
    −
    3
    x
    +
    1
    		)
  • (
    −
    3
    x
    −
    1
    		)
Question 6
6.
    • Factorize
    •  
    • (
      a
      −
      b
      		)
      3
      		  +  
      (
      b
      −
      c
      		)
      3
      		  +  
      (
      c
      −
      a
      		)
      3
      • 3
      • (
        a
        −
        b
        		)
      • (
        b
        −
        c
        		)
      • (
        c
        −
        a
        		)
      • 3
      • (
        a
        −
        b
        		)
      • (
        b
        +
        c
        		)
      • (
        c
        −
        a
        		)
      • 3
      • (
        a
        −
        b
        		)
      • (
        b
        +
        c
        		)
      • (
        c
        +
        a
        		)
      • 3
      • (
        a
        +
        b
        		)
      • (
        b
        −
        c
        		)
      • (
        c
        −
        a
        		)
      • 3
      • (
        a
        −
        b
        		)
      • (
        b
        −
        c
        		)
      • (
        c
        +
        a
        		)
Question 7
7.
    • Factorize
    •  
    		•
      a
      2
      		  −  
      b
      2
      		  −  
      c
      2
      		  −  
      2
      b
      c
      • (
        a
        −
        b
        −
        c
        		)
      • (
        a
        +
        b
        −
        c
        		)
      • (
        a
        −
        b
        −
        c
        		)
      • (
        a
        +
        b
        +
        c
        		)
      • (
        a
        +
        b
        +
        c
        		)
      • (
        a
        +
        b
        −
        c
        		)
      • (
        a
        +
        b
        +
        c
        		)
      • (
        a
        −
        b
        +
        c
        		)
      • (
        a
        −
        b
        −
        c
        		)
      • (
        a
        −
        b
        +
        c
        		)
Question 8
8.
    • The degree of polynomial
    • (
      −
      6
      c
      3
       
      d
      3
       
      +
      5
      c
      3
       
      d
      2
       
      e
      +
      c
      3
       
      d
      +
      5
      c
      2
       
      d
      3
       
      e
      2
       
      +
      6
      c
      e
      −
      8
      c
      −
      8
      e
      3
       
      		)
    • is
  • 4
  • 9
  • 8
  • 7
  • 6
Question 9
9.
Which of the following algebraic expressions is a binomial?
  • (
    7
    b
    3
     
    c
    3
     
    −
    7
    b
    3
     
    c
    −
    5
    b
    c
    3
     
    		)
  • (
    7
    a
    3
     
    b
    2
     
    +
    a
    2
     
    b
    c
    2
     
    −
    5
    a
    b
    3
     
    c
    3
     
    +
    6
    b
    2
     
    c
    2
     
    		)
  • (
    −
    7
    a
    3
     
    c
    2
     
    −
    3
    b
    c
    3
     
    		)
  • (
    −
    5
    a
    3
     
    b
    3
     
    c
    −
    4
    a
    b
    2
     
    c
    −
    7
    a
    b
    +
    5
    b
    3
     
    c
    		)
  • (
    −
    a
    b
    c
    2
     
    		)
Question 10
10.
    • Given
    • f
      (
      m
      )
    • =
    • (
      m
      2
       
      +
      4
      m
      −
      7
      		)
    • ,
    • find
    •  
    • f
      (
      (-3)
      )
  • -8
  • -12
  • -9
  • -10
  • -11