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Common Errors Committed  by the  Students  in Secondary Mathematics   Errors  that students often make in doing secondary mathematics  during their practice and during the examinations  and their remedial measures are well explained here stp by step.  Some Common Errors in Mathematics

Math Assignment Class IX Ch-2 | Polynomials

 Maths Assignment Class 9th 
Chapter 2  Polynomials

Mathematics Assignment for Class IX Ch -2, Polynomials, strictly according to the CBSE syllabus. Math worksheet based on the topic Polynomial. 

Mathematics Assignment on Polynomials 

Class IX Chapter 2

1. Find the value of p(x) = 3x- 2x + 8 at

a)  x = 0        Ans : 8
b)  x = -2      Ans : 24  
c)  x = 3        Ans : 29
d)  x = -5      Ans : 73

2. Find the remainder when x- 3x+ 3x - 1 is  divided by

a)     x - 1         Ans 0
b)   x + 1         Ans -8                                





f)    3-x           Ans 8

Q 3. a) Show that 2x - 3 is a factor of  P(x) = 2x- 9x+ x + 12.
Ans: P(3/2) = 0  ⇒ 2x - 3 is the factor of P(x)

   b) Show that x + 2 is a factor of  P(x) = x- x- 12.

Ans: P(-2) = 0  ⇒ x + 2 is the factor of P(x)

Hint: If remainder = 0 then given function is the factor of the given polynomial otherwise not.


4. Find the value of k if x + 1 is a factor of
a) 3x – kx + √3         Ans   -3 - √3
b) √2x – kx + k + 2  Ans  
c) k – kx + Kx         Ans 0
d) x - 3x + kx          Ans - 4
Q5) Find “a” if x+1 is a factor of P(x) = ax3 - 9x2 + x + 6a        Ans:- 2

Solution Hint: Let x + 1 = 0 ⇒ x = - 1
Now find  P(-1) by putting x = -1 in p(x)
If P(-1) = 0 then x + 1 is the factor of p(x) otherwise not
Q 6) If (x -2)and(x + 3) are factors of p(x) = ax+ 3x- bx - 12.  Find a and b.     
Ans: a = 1, b = 4

Solution Hint :
x - 2 is the factor of P(x) ⇒ P(2) = 0
a(2)3  + 3(2)2  - b(2) - 12 = 0
                                      8a -2b = 0
                                         4a -b = 0 ....... (i)
x + 3 is the factor of P(x) ⇒ P(-3) = 0
a(-3)3  + 3(-3)2  - b(-3) - 12 = 0
                -27a + 27 + 3b - 12 = 0
                                          -9a +b = -5 ....... (ii)
Eqn.(i) -Eqn(ii) we get




                       






                      ⇒ a = 1
Putting  a = 1 in eqn. (i) we get
4(1) -b = 0 ⇒ b = 4

Q 7. If x - 5 is a factor of x+ ax+ bx - 20  and leaves a remainder -2 when divided by x - 3. Find a and b.
Ans (-9, 24)

Solution Hint
x - 5 is the factor of P(x) ⇒ P(5) = 0
(5)+ a(5)+ b(5) - 20 = 0
5a + b = -21 ...... (i)
Also  P(3) = -2
(3)+ a(3)+ b(3) - 20 = 0
3a + b = -3 ........ (ii)
Eqn.(i) -Eqn.(ii) we get









                  ⇒ a = -9
Putting  a = -9 in eqn. (ii) we get
3(-9) + b = -3 ⇒ b = 24

Q 8. Factorize:

a) x+ 11x + 30      : Ans  (x + 5)(x + 6)

b) a- 16a + 63       : Ans  (a - 7)(a - 9)

c)15 - 2x - x2           : Ans    (3 - x)(5 + x)

d) 3 + 5x - 2x2       : Ans   (1+ 2x)(3 - x)                                                        

e) 3m- 20m - 7   : Ans  (3m+1)(m - 7)                            

f) 24m+ m - 23      : Ans (m + 1)(24m - 23)

g) 2x+ 11xy - 21y    : Ans    (x + 7y)(2x - 3y)                            

h) 7(x + y)2 + 48(x + y) - 7       : Ans  (x + y + 7)(7x + 7y - 1)

I) 2m4n - 6m2n + 4n                 : Ans  2n(m+1)(m-1)(m2-2)                        

 j) 36(a+3b)- 36(2a-3b)2   : Ans  (16a+3b)(33b-4a)

k) x+ 3x- 4x - 12                   : Ans (x - 2)(x + 2)(x + 3)                          

l) 2x- 9x +x + 12                   : Ans  (x + 1)(x - 4)(2x - 3)

m) x-3x-10x+24              : Ans   (x + 3)(x - 4)(3x - 2)                            

n) 2x-7x- 3x + 18               : Ans  (x - 2)(x - 3)(2x + 3)

o) 3x+ x - 38x + 24               : Ans   (x - 3)(x + 4)(3x - 2)                          

p)(x3 - (y - z)3)              : Ans  (x – y + z)(x2 + y2 + z2 - 2yz – xy - xz)

  

9.  Evaluate by using identity:

a)   92×108        Ans:- 9936

b)  6.7×5.3        Ans:- 35.51

c)104×107        Ans:- 11128

10.Factorize:

a)  8x- 125y- z- 30xyz                            

b)  125x- 8 + 27y+ 90xy      

c)  3√3a3 - 5√5b3 - 8c3 - 6√15abc           

d)  (5a - 4b)3 + (4b - 6c)+ (6c - 5a)3

e)  a+ (a - 1)+ (1 - 2a)3                                                     

f)  (3x + 3y - 5z)+ (2y + 3z - 5x)+ (2z + 2x - 5y)3

g)  (2x + y)3 - (x + y)3                      

h)  64m6-n6  : Ans:  (2mn + n)(4m - 2mn + n)(2m - n)(4m + 2mn + n)

11.Evaluate by using identity:

a)  (-15)3 + (-13)3 + (28)3     Ans: 16380
b)  (75)3 + (-50)3 + (-25)3    Ans: 281250

12.Simplify:  
       

Q13.If   a = 1 - √2, find  the value of    Ans: 8

Q 14.) 
If a+ b+ c= 3abc  and a + b + c = 0 then show that



Q15.)
If              
16.  Evaluate:  
17.  If     =  83, then find          Ans:  756
18.  If   , then find the value of        Ans: 52
19).  If    ,  then find the value of       Ans: 36
20.  If  , then find the value of      Ans : equation 
21.  Find the value of                Ans : 
22.  If  , then find the value of         Ans:  equation
23.  If   , then find          
24)  If    , then find            [Ans 6 ]
25.  Find the remainder when x4 + 3x2 + 3x + 1 is divided by x + 1   [Ans : 2]

26.  If x3 + ax2+ bx + 6 has (x - 2) as a factor and leaves remainder 3, when divided by (x – 3), find a and b      Ans[a = -3, b = -1]

27.  For what value of a is 2x3 + ax2 + 11x + a + 3 divided by 2x - 1     Ans[a = -7 ]


THANKS FOR YOUR VISIT
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Comments

  1. Very very nice assigament, thank ku so much.

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