The document contains a multiple choice test on polynomials with 50 questions. The questions cover topics such as identifying polynomials, finding zeroes of polynomials, factorizing polynomials, and evaluating polynomials. The test also includes some word problems involving polynomials. The answers to all 50 questions are provided at the end.

1. MULTIPLE CHOICE QUESTIONS
1. Which one of the following is a polynomial?
(a) (b) 2x 1 ( c ) 2 + 3 r 2
(d)
2. 2 is a
polynomial ofdegree
(a) 2 (b) 0 (c)1 (d)
126 Mathematics-9

2. Degree ofthe polynomial 4r" +0. xs +0.x2 + 5x + 7 is
(b)5 (c) 3 (d) 7
(a) 4
4, Degree ofthe zero polynomial is
(a) 0 (b)1
(c) any natural number (d) not defined
5.Ifp)= -2/2x + 1, then P(2/2) is equal to
(c) 4
(b) 1 d) 8v2 +1
(a)0
6, The value ofthe polynomial Sx -4x +3, when x =
-1 is
(b) 6
(a) -6 (c) 2 (d) -2
7. Ifp(x) =x* 3, then p(x) +p(-x) is equal to:
(b) 2x
(a) 3 (c) 0 (d) 6
8. Zero of the zero polynomial is :
(b) 1
(a) 0 (c) any real number (d) not defined
9. Zero of the polynomial p(x) = 2x + 5 is:
(a) (b) ()
(d)2
10. One of the zeroes of the polynomial 2x2 + 7x - 4 is
(a) 2 (b) () (d)-2
11. If3 + 51 is divided by x + 1, the remainder is
(c) 49
(a) 0 (b) 1 (d) 50
12. Ifx + 1 is a factor of the polynomial 2x + kx, then the value of k is:
(d)-2
(a)-3 (b) 4 (c) 2
13. x+ 1 is a factor ofthe polynomial
(a) x+ -x +1
c)+ +*+1
(b)3+x + x+ 1
(d)+3+ 3x +x +1
4. One
ofthe factors of(252 -
1) +(1 + 5x) is
(a) 5+x (b) 5 - x (c) Sx - 1 (d) 10x
15, The value of 2492 -
2482 is :
(a) 12 (b) 477 (c) 487 (d) 497
6. The factorisation of 4x2 + 8x + 3
(a) (x +1(x + 3)
(c) (2x +2)(2x +
5)
17. Which of the following is a factor of (r+ y -(r +y')?
IS
(b) (2r + 1)(2x + 3)
(d) (2r - 1) (2 3)
(a)+y2 +
2xy (b) x+- xy (c) xy (d) 3xy
Polynomials 127

3. 18. The coefficient of x in the expansion of (r + 3)° 1s
(c) 18
(a) 1 (b) 9 (d) 27
19. If + =
-1 (x, y * 0), then value of x' -
ys is :
(a) 1 (b) -1 (c) 0 (d)
20. If 492 b =
|7x- then the value of b is
(a) 0 (d)
21. If a +b +c = 0, then a' + b3 + c$ is equal to0
(a) 0 (b) abe (c) 3abc (d) 2abc
22. If2+ kx + 6 (x +2)(x +3), for all x, then the value of k is:
(a) 1 (b) -1 (c) 5 (d) 3
23. Zero of the polynomial p(x) = (cx + d) is
(a) d (b)-c
d
(c) (d)
C
24. Zero of the polynomial plr) = a'x, a #0 is:
(a) 0 (b) 1 (c) -1 (d) a
25. Zero of the polynomial p(x), where plr) = ax + 1, a * 0 is
(
(a)- (b)0 (d) - a
a a
26. The remainder whenxs + 3x +3x +1is divided by 5+2x is:
(a)27
8
(b)23
5
d)
27. The remainder when xs + 3x + 3x + 1 is divided by x is
(a) -1 (b) 1 (d) 2
28. The remainder when xs + 3x +3x + 1 is divided by x + t is:
(a) -T+ 32 3t +1
(c) T + 32 3t -
1
(b) T3 3T23t -1
(d) -T3 + 37 - 1
29. When 6x2 + ar + 7 is divided by x 2, the remainder is 3. The half of a is
(a)-8 (b) -7 (c) 6 (d) 10
30. Ifx -2 is a factor of r - 2axd t ax - 1, then the value of a is
(a) (b) (c) (d)
31. The value of k, if x - T is a factor of p(r) = kx2 - 2x + I is
(a) 2 (b) 2+1 (c) V2 - 1
(d)
32. Ifx+ I is a factor ofax + x* -
2x + 4a-9, then the value of a =
(a) 1 (b) 2 (c) 3 (d) 1
128
M a t h e m a t i c s -

4. 33 Ifx- = 1 and x +y =
41, then x +y =
(a) +6 (b) +9 (c) 16 (d) +25
= 47, then the value of x +
34. If +
(a) 3 (b) 5 (c) 7 (d) 11
35.Ifx- 5,then42+
(a) 9 (b) 16 (c) 25 (d) 64
6. If3a + 4b =
16 and ab =
4, then 9a +1662 =
(a) 140 (b) 150 (c) 160 (d) 170
7, Ifa +b + c
=
4 and ab + be + ca =
6, then a3 + b3 + c3-3abc
(a)-6
(b) -7 (c)-8 (d) 10
38. If7 +t m +n =
0, then +
mn nl Im
(a) 1
(b) 2 (c) 3 (d) 4
39. If+=-1, then the value of r3-y
(a) 0
(b) -1 (c) (d)
40. The value ofxs + ys -
12xy + 64, when x + y
= -
4 is
(a) 0
(b) 1 (c) (d
41. Ifa +b +c =
5 and ab + bc + ca
=
10, then as +b3 + c3 -
3abc =
(d) 30
(a) -15
(b)-20
(c)-25
42. Ifx+ 3, then thevalue of x* +
.
(c)-7
(d)-8
(a) 7
(b) 8
43. If x + =
4, then the value of x* +
(c) 52
(d) 60
(a) 50
(b) 48
. If both x + 1 and x 1 are
factors ofar +r -
2r + b, then a + b =
(a) 1
(c) -1
(d) 3
(b)-2
.
If(r +2) and ( -
1) are
factors ofthe
polynomial lOr +pr +q. then , is:
(d)-2
1
(b)
(c)-1
(a 4
40. If a + b? + 2 = 90 and a + b +c
=
20, then the value of ab + bc + ca
=
(a) 155
(c) 165
(d) 170
, I f a +b + c
=
3, a? + b2 + cé= 5 and a't
* c=9,
then the value ofabe =
(a) 0
(b) 160
(c) 2
(d) -1
. Without actually
calculating
the
cubes,
the
value
of(0.2)"
-
(0.3)3+ (0.1)3 =
(a) 0.018
(b) 1
(c) 0.019
(d) -0.019
(b) 0.018
129
Polynomials

5. 49. If a2 + b2 + c2 200 and ab + bc + ca = 28, then the value of a tb+c, is :
(a) 156 (b) 256 (c) 16 (d) 320
50. If(x -
a) is a factor ofx3- mx2 -
2xan +
na?: a 0, then a
(a) m +n (b) m -
n (c) (d) mn
ANSWERS
1. () 2. (b) 3. (a) 4. (d) 5. (b) 6. (a) 7. (d) 8. (c) 9. (b) 10. (6)
11. (d) 12. (c) 13. (b) 14. (d) 15. (d) 16. (b) 17. (d) 18. (d) 19. (c) 20. ()
22. (c) 23. (c) 24. (a) 25. (a) 26. (a) 27. (b) 28. (a) 29. (b) 30. (6)
32. (b) 33. (b) 34. (a) 35. (a) 36. (c) 37. (c) 38. (c) 39. (a) 40. (a)
44. (a) 45. (a) 46. (a) 47. (a) 48. (a) 49. (c) 50. ()
21. (c)
31. (c)
41. (c) 42. (a) 43. (c)
s L V DAecn OLICCTIONC

6. SELFEVALUATION TEST
PART-A
Section-I
(Question numbers 1 to 10 carry 1 mark each.)
1. Is x +5 a
polynomial?
-x+3x+5
2. Find the coefficient of x in
TT
3. Is -12 a constant polynomial?
4. Write a monomial of degree 1000.
5.
lfx +y =
8 and y
=
6, then find x' + '.
6. Find (r + 9* -12) using suitable identity
7. Show that (r + 3) is a factor ofthe polynomial.,p() =x +r - 7x2-x +6
8. Find zeroes ofthe polynomial, p(t) =
(x + 1)x -
2)x+ 3)
9. Show that x + 4x + 7 has no zero.
10. If p(x) = 4x3 - 3x + 2x - 4, evaluate p(2)
P(0) x p(1)
Section-II
(Question no. 11 is a Case Study Based Question. It contains 5 subparts.
Each subpart carries 1 mark.)
11. Two friends Rashi and Pragya were given a
polynomial by their
maths teacher. POLYNOMIALS
The polynomial was P(x) =x* -
5x +6. Coefficient
EXponent
Answer the following questions. Constant
(i) The given polynomial is a : 5x+6
(a) linear polynomial Variable
(b) quadratic polynomial
(c) trinomial
(d) both (b) and (c)
(ii) Zeroes of this polynomial are
(a) 2, -3 (b) 2, 3
(c)-2,-3 (d)-2,3
(iii) Value ofthe polynomial when x =
-1 is
(a) 12 (b) 13 (c) 14 (d) -12
iv) Value of P(3) + P(1) =
(a) 0 (b) I (c)2
(d) 3
(V) A quadratic polynomial
(a) have always 2 zeroes
(b) may have more than 2 zeroes
(c) have exactly one zero
(d) may have no zero
132 M a t h e m a t i c s - 9

7. PART-B
(Question numbers 12 to 14 carry 2 marks each.)
12. Factorise:(i) 12x- 7x + 1 (i) 3x2-x - 4
13. Factorise :(i) 49a + 70ab + 25b2
14. Factorise: 4x + +z2 - 4xy - 2yz + 4xz
(Question numbers 15 to 18 carry 3 marks each.)
15. Verify ()*+y =(x + y) ( - xy + ) (i) x3-y3 =
=(* -y)( +ay + )
16. Ifx
+y +z =
0, show that +y3 +2 =
3xyz
17. Verifythat: x3+y3 +z3 -
3xyz = +y +
z)(x -y) +
(y- z)} +
( -x)1|
18. Factorise
(i) 4x + 9+16z2 + 12xy 24yz 16xz (i) 22+ y? + 82-2 2 xy + 4 2 yz - 8xz
(Question numbers 19 to 21 carry 4 marks each.)
19. Prove that (a + b +
c - a' -
b -
cd =
3(a +
b(b + cc + a)
-+(-*
(x-y +(y- =* +(: -x*
20. Simplify
ab c =3
21. If a, b, c are all non-zero and a + b + c = 0, prove that
bc Ca ab
ANSWERS
1. No 3. Yes 4. 1000 5. 368 6. x-3x - 108 8.-1, 2,3
10. 5 11. ) (d) (ii) (6) (i) (a) (iv) (c) (V) (d) 12. (i) (3x -
1)4x -
1) Gi) (x + 1)(3x -
4)
13. () (7a + 5b) (7a + 5b) (i) 14. (2x-y +
z)(2x -y +
z)
18. ) (2r +3 4: 2x + 3y- 42) (n-V2x+y + 2/2z)-V2x + y + 2/2z)
20. r+ y)y + z0z + x)