### Mathematics Assignments | PDF | 8 to 12

PDF Files of Mathematics Assignments From VIII Standard to XII Standard PDF of mathematics Assignments for the students from VIII standard to XII standard.These assignments are strictly according to the CBSE and DAV Board Final question Papers

## 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.

## 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

$\large \bg{black}\mathbf{c)\: \: x-\frac{1}{2}\: \: \:\: \: Ans\: \frac{-1}{2}}$

$\large \bg{black}\mathbf{d)\: \: 2x+1\: \: \:\: \: Ans\: \frac{-27}{8}}$

$\large \bg{black}\mathbf{e)\: \: 5-2x\: \: \:\: \: Ans\: \frac{27}{8}}$

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) 3
x2 – kx + √3         Ans   -3 - √3
b) √2
x2 – kx + k + 2    Ans
$\large \bg{black}\mathbf{-\frac{1}{2}(2+\sqrt{2})}$
c) k – kx2 + Kx         Ans:  0
d)
x2 - 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. 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)(m- 2)

j) 36(a + 3b)- 36(2a - 3b)2      : Ans  108a(- a + 6b)

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

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

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

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

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

$\large \bg{black}\mathbf{p)\: \: 27p^{3}-\frac{1}{216}-\frac{9}{2}p^{2}+\frac{1}{4}p\: \: \: Ans:\; \left ( 3p-\frac{1}{6} \right )^{3}}$

7.  Evaluate by using identity:

a)   92 × 108        Ans:- 9936

b)  6.7 × 5.3        Ans:- 35.51

c)104 × 107        Ans:- 11128

8.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)

Question 9.Evaluate by using identity:

a)  (-15)3 + (-13)3 + (28)3     Ans: 16380

b)  (75)3 + (-50)3 + (-25)3    Ans: 281250

Question 10: For what value of a if 2x3 + ax2 + 11x + a + 3 is divided by 2x - 1
Ans[a = -7 ]
Question 11: Find the remainder when x4 + 3x2 + 3x + 1 is divided by x + 1
[Ans : 2]

Question 12.
If (x - 2)and(x + 3) are factors of p(x) = ax3  + 3x2  - 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

4a - b = 0
-9a + b = -5
----------------
-5a   = -5
⇒ a = 1
Putting  a = 1 in eqn. (i) we get
4(1) -b = 0 ⇒ b = 4
Question 13.
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

5a + b = -21
3a b =  3
-----------------
2a       =  -18
a   =  - 9

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

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]

HIGHER ORDER THINKING SKILL
HOTS
Q 14.) If a+ b+ c= 3abc  and a + b + c = 0 then show that

$\bg{black}\mathbf{\frac{(b+c)^{2}}{3bc}+\frac{(a+c)^{2}}{3ac}+\frac{(b+a)^{2}}{3ba}=1}$
Q15.)
If
$\bg{black}\mathbf{x^{2}+\frac{1}{x^{2}}=14 ,\: \: find\: \: x^{3}+\frac{1}{x^{3}}}$          $\bg{black}\mathbf{Ans\: \: \pm 52}$
16.  Evaluate:

$\bg{black}\mathbf{\left ( \frac{x^{a}}{x^{b}} \right )^{a+b}\times \left ( \frac{x^{b}}{x^{c}} \right )^{b+c}\times \left ( \frac{x^{c}}{x^{a}} \right )^{c+a}\: \: \: Ans:\: 1}$
17.  If   $\bg{black}\mathbf{x^{2}+\frac{1}{x^{2}}}$  =  83, then find   $\bg{black}\mathbf{x^{3}-\frac{1}{x^{3}}}$       Ans:  756
18.  If   $\bg{black}\mathbf{x=2+\sqrt{3}}$, then find the value of   $\bg{black}\mathbf{x^{3}+\frac{1}{x^{3}}}$     Ans: 52
19).  If    $\bg{black}\mathbf{x-\frac{1}{x}=3}$,  then find the value of  $\bg{black}\mathbf{x^{3}-\frac{1}{x^{3}}}$     Ans: 36
20.  If  $\bg{black}\mathbf{x=3+2\sqrt{2}}$, then find the value of  $\bg{black}\mathbf{x^{3}-\frac{1}{x^{3}}}$    Ans : $140\sqrt{2}$
21.  Find the value of    $\large \bg{black}\mathbf{\sqrt[4]{\sqrt[3]{\sqrt{2^{2}}}}}$            Ans :  $2^{1/12}$
22.  If  $x=3+2\sqrt{2}$, then find the value of   $\sqrt{x}+\frac{1}{\sqrt{x}}$      Ans:  $2\sqrt{2}$
23.  If  $a=\frac{3+\sqrt{7}}{2}$ , then find   $a^{2}+\frac{1}{a^{2}}$       $\bg{black}\mathbf{\left [ Ans:\: 20-\frac{9}{2}\sqrt{7} \right ]}$
24)  If    $\bg{black}\mathbf{a=\frac{4}{3-\sqrt{5}}}$, then find   $a+\frac{4}{a}$         [Ans 6 ]
25 .Simplify:

$\bg{black}\mathbf{\left ( 1-\frac{1}{x+1} \right )\left ( 1-\frac{1}{x+2} \right )\left ( 1-\frac{1}{x+3} \right )\: ......\: \left ( 1-\frac{1}{x+10} \right )}$       $\bg{black}\mathbf{Ans\: \left ( \frac{x}{x+10} \right )}$
26. If   a = 1 - √2, find  the value of $\bg{black}\mathbf{\left ( a-\frac{1}{a} \right )^{3}}$   Ans: 8

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