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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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