Polynomials Class 9 MCQ with Answers – Maths Class 9 MCQ Online Test are covered in this Article. Polynomials Class 9 MCQ Test contains 30 questions. Answers to MCQ on Polynomials Class 9 are available after clicking on the answer. MCQ Questions for Class 9 with Answers have been made for Class 9 students to help check the concept you have learnt from detailed classroom sessions and application of your knowledge.
| Board | CBSE |
| Textbook | Maths (NCERT) |
| Class | Class 9 |
| Chapter | Chapter 2 Polynomials |
| Category | MCQ Questions for Class 9 Maths with Answers |
Polynomials Class 9 MCQ with Answers
1. The constant polynomial 0 is a
(a) Linear polynomial
(b) Zero polynomial
(c) Quadratic polynomial
(d) Monomial polynomial
Answer
Answer: (b) Zero polynomial
2. The degree of the polynomial (x2 – 1) (x3– x4– x +1) is
(a) 3
(b) 4
(c) 5
(d) 6
Answer
Answer: (d) 6
Explanation: The highest degree variable in first bracket is x2 and in second bracket is x4 on multiplying x2 with x4.the highest power we obtain is 6.
3. A zero of a polynomial need to be 0.
(a) True
(b) False
Answer
Answer: (b) False
Explanation: A zero of a polynomial need not to be 0.
4. The zeroes of the quadratic polynomial x2 + 4x +4 are
(a) both positive
(b) both negative
(c) one positive and one negative
(d) both equal
Answer
Answer: (b) both negative
Explanation:
p(x)=x2 + 4x +4
x2 + 4x +4 =0
x2 + 2x +2x+4=0
x(x+2) +2(x+2) =0
(x+2) (x+2) =0
X= -2; -2
5. The zeroes of polynomial depend on its
(a) No. of terms
(b) Degree
(c) Both
(d) None
Answer
Answer: (b) Degree
Explanation:
| polynomial | Degree | zeroes
|
| Linear | 1 | 1 |
| Quadratic | 2 | 2 |
| Cubic | 3 | 3 |
| ……so on |
6. Find the zero of the polynomial 3x + 4.
(a) -4/3
(b) 3
(c) 4
(d) -3/4
Answer
Answer: (a) -4/3
Explanation:
p(x) = 0
3x +4 =0
x = -4/3
7. The polynomial of degree 3 has at most how many zeroes
(a) 3
(b) 2
(c) 1
(D) 0
Answer
Answer: (a) 3
8. The zeroes of the quadratic polynomial 6x² + 11x – 35 are
(a) both positive
(b) both negative
(c) one positive and one negative
(d) both equal
Answer
Answer: (c) one positive and one negative
Explanation:
p(x)= 6x² + 11x – 35
6x² + 11x – 35 =0
6x² + 21x – 10x – 35 =0
3x(2x+7) -5(2x+7) =0
(2x+7) (3x-5) =0
X= -7/2; 5/3
9. If the zeroes of the quadratic polynomial x2– ax + b are 5 and –7, then
(a) a = –2, b = –10
(b) a = 5, b = –10
(c) a = -2, b = –35
(d) a = 7, b = – 6
Answer
Answer: (c) a = -2, b = –35
Explanation:
p(x)= x2 – ax + b
When, p (5) = 52 – 5a + b = 25 -5a + b
=> 5a – b = 25…………(i)
P (-7) = (-7)2 + 7a + b = 49 + 7a +b
=> 7a + b = -49 ………..(ii)
From adding (i) & (ii), we get
12a = – 24
=> a = -2
Putting the value of a in (ii),
7 × (-2) + b = -49
=> b = -49 + 14 = -35
10. Find p (-1), for (x3– 1).
(a) 2
(b) -1
(c) -2
(d) 0
Answer
Answer: (c) -2
Explanation:
p(x) = x3– 1
P (-1) = (-1)3 -1 = -1 -1 = -2
Polynomials Class 9 MCQ with Answers
11. Check whether x = -1/√3 is a zero of which polynomial
(a) -2x +3
(b) -3x + 1
(c) X2 + 3
(d) 3x2 – 1
Answer
Answer: (d) 3x2 – 1
Explanation:
p(x) = 3x2 – 1
P ((-1)/(√3)) = 3 × ((-1)/(√3))2 – 1 = 3 × 1/3 – 1 = 1-1 = 0
13. If (x+1) is a factor of polynomial 3x 2 -9x +k, Find the value of k.
(a) -12
(b) 6
(c) 3
(d) -6
Answer
Answer: (a) -12
Explanation:
p(x) = 3x2 -9x +k
If (x+1) is a factor of polynomial 3x2 -9x +k
Then, x+1 = 0
x = -1 is a zero of the polynomial.
p (-1) = 3(-1)2 -9×(-1) +k = 3 + 9 +k = 12+k
12+ k = 0
K = -12
14. bx 2 + cx + a is a polynomial with …………variables.
(a) four
(b) three
(c) two
(d) one
Answer
Answer: (d) one
Explanation: The polynomial bx2 + cx1 + ax0, has only x variable with powers as whole numbers 2,1,0.
15. The value of p(t)= t2-7t+2, when t = -2 is
(a) -25
(b) 20
(c) 51
(d) 34
Answer
Answer: (b) 20
Explanation:
p(t)= t2-7t+2
P (-2) = (-2)2 – 7(-2) +2 = 4 +14 +2 = 20
16. Factorize x2-8x+15, by splitting method.
(a) (x -3) (x-5)
(b) (x +3) (x+5)
(c) (x-15) (x-1)
(d) (x+1) (3x+5)
Answer
Answer: (a) (x -3) (x-5)
Explanation: x2-8x+15
Here, a +b = -8, ab = 15
So, the possible factor is (3,5)
x2-8x+15 = x2 – 3x – 5x +15 = x(x-3) -5(x-3) = (x-3) (x-5)
17. x2 – y2 =…………..
(a) x2 -2xy + y2
(b) (y + x) (y-x)
(c) (x+ y) (x-y)
(d) 1
Answer
Answer: (c) (x+ y) (x-y)
18. The number of polynomials having two zeroes 2 and -1 is
(a) 1
(b) 2
(c) 3
(d) infinite
Answer
Answer: (d) infinite
Explanation: The formed quadratic polynomial having two zeroes is infinite.
19. (x + a) (x-b) = ………………
(a) x2 + (a – b) x + ab
(b) x2 + (a – b) x – ab
(c) x2 + (a + b) x + ab
(d) x2 + (a + b) x – ab
Answer
Answer: (b) x2 + (a – b) x – ab
Explanation: (x+ a) (x-b) = x2 + ax – bx – ab = x2 + (a – b) x – ab
20. Expand (4a – 5b +6c )2
(a) 16a2 + 25b2 + 36c2 – 40ab + 60bc + 48ca
(b) 8a2 + 25b2 + 16c2 – 40ab – 60bc + 48ca
(c) 16a2 + 25b2 + 36c2 – 40ab – 60bc + 48ca
(d) None of the above
Answer
Answer: (c) 16a2 + 25b2 + 36c2 – 40ab – 60bc + 48ca
Explanation:
Using, (x +y +z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx
(4a – 5b +6c )2 = (4a)2 + (-5b)2 + (6c)2 + 2 x4a x(-5b) + 2 x(-5b) x6c + 2 x6c x4a
= 16a2 + 25b2 + 36c2 – 40ab – 60bc + 48ca
Polynomials Class 9 MCQ with Answers
21. 27x3 + 125y3 = (3x + 5y) ………….
(a) (9x2 + 25y2 +15xy)
(b) (3x + 5y) (9x2 + 25y2 -15xy)
(c) (3x – 5y)2
(d) (9x2 + 25y2 -15xy)
Answer
Answer: (d) (9x2 + 25y2 -15xy)
Explanation:
Using, x3 + y3 = (x+ y)3 – 3xy (x+ y)
27x3 + 125y3 = (3x)3 + (5y)3
= (3x + 5y)3 – 3×3x × 5y (3x + 5y)
= (3x + 5y)3 – 45xy (3x + 5y)
= (3x + 5y) {(3x + 5y)2 – 45xy}
[(a+ b)2 = a2+ b2 +2ab]
= (3x + 5y) [{(3x)2 + (5y)2 + 2(3x) (5y)} – 45xy]
= (3x + 5y) {9x2 + 25y2 + 30xy – 45xy}
= (3x + 5y) (9x2 + 25y2 -15xy)
22. If one of the zeroes of the quadratic polynomial (k+1) x² + k x + 1 is – 3, then the value of k is
(a) 4
(b) 3/5
(c) -5/3
(d) -5
Answer
Answer: (c) -5/3
Explanation:
p(x)= (k+1) x² + k x + 1
P (-3) = 0
(k+1) (-3) ² + k (-3) + 1 = 0
9k + 9 -3k +1 = 0
6k + 10 = 0
k = – 10/6 = – 5/3
23. If one of the zero of the quadratic polynomial ax² + bx is zero, the other zero is
(a) a
(b) -b/a
(c) c/a
(d) 0
Answer
Answer: (b) -b/a
Explanation:
p(x) = ax² + bx
P (0) = 0
ax² + bx = 0
ax² = – bx
x = – b/a
24. Expand (6p – 7q)3
(a) 216p3 – 343q3
(b) 36p3 – 49q3 – 56p2q + 82pq2
(c) 216p3 – 343q3 – 756p2q + 882pq2
(d) 216p3 – 343q3 + 756p2q + 882pq2
Answer
Answer: (c) 216p3 – 343q3 – 756p2q + 882pq2
Explanation:
Using, (a-b)3 = a3 – b3 – 3ab (a – b)
(6p – 7q)3 = (6p)3 – (7q)3 – 3(6p) (7q) (6p – 7q)
= 216p3 – 343q3 – 126pq (6p – 7q) = 216p3 – 343q3 -756p2q + 882pq2
25. Evaluate 107 x 93.
(a) 9951
(b) 1091
(c) 9091
(d) 9591
Answer
Answer: (a) 9951
Explanation:
107 x 93 = (100+7) x (100-7)
Using, (a + b) (a-b) = a2 – b2
(100+7) x (100-7) = (100)2 – (7)2 = 10000 – 49 = 9951
26. If a and b are the zeroes of quadratic polynomial x2+x-6, then
(a) a +b =ab
(b) a – b =ab
(c) a +b >ab
(d) a + b <ab
Answer
Answer: (c) a +b >ab
Explanation:
x2+x-6
| P(a)= x2+x-6 | P(b)= x2+x-6 |
| a2+a-6 = 0
a2+3a – 2a -6= 0 a (a+3) -2(a+3) = 0 (a+3) (a-2) = 0 a = -3 ,2 |
b2+b-6 = 0
b2+3b – 2b -6= 0 b (b+3) -2(b+3) = 0 (b+3) (b-2) = 0 b = -3 ,2 |
Let,
| a= -3, b=2 | a= 2, b = -3 |
| a +b= -3+2 = -1
a-b = -3-2 = -5 ab = (-3) × 2= -6 |
a +b = 2 -3 = -1
a-b = 2+3 = 5 ab = -6 |
a + b >ab = -1>-6
27. Evaluate 173 – 193
(a) -1946
(b) 1938
(c) 1946
(d) 946
Answer
Answer: (a) -1946
Explanation:
Using, a3 – b3= (a-b)3 +3ab(a-b)
173 – 193 = (17-19)3 + 3 × 17 ×19 (17 -19)
= (-2)3 + 3×17×19×(-2)
= -8 – 1938
= – 1946
28. Factorize: 3x2 + 5y2 + 4z2 + 2√15 x y – 4√5yz – 4√3zx
(a) (√3x – √5y – 2z )2
(b) (√3x + √5y + 2z )2
(c) (√3x + √5y – 2z )2
(d) (√3x – √5y + 2z )2
Answer
Answer: (c) (√3x + √5y – 2z )2
Explanation:
3x2 + 5y2 + 4z2 + 2√15 x y – 4√5yz – 4√3zx
= (√3x)2 + (√5y)2 + (-2z)2 + 2(√3x) (√5y) + 2(√5y) (-2z) + 2(-2z) (√3x)
Using, (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz +2zx
= (√3x + √5y – 2z )2
29. Find the zero of the polynomial: px + q
(a) -p/q
(b) p/q
(c) -1
(d) -q/p
Answer
Answer: (d) -q/p
Explanation: p(x) = px +q
px +q = 0
x = -q/p
30. If p and q are zeroes of polynomial 3x2-4x-4, then find p +q + p q.
(a) -4/3
(b) 3/4
(c) 0
(d) 2/3
Answer
Answer: (c) 0
Explanation:
p(x)= 3x2-4x-4
3x2-4x-4 = 0
3x2– 4x – 4 =0
3X2 – 6x + 2x – 4 = 0
3x (x-2) +2 (x-2) =0
(x-2) (3x+2) =0
X = 2, -2/3
p + q +p q = 2 + ((-2)/3) + 2((-2)/3)
= 2 – 2/3 – 4/3
= 0
MCQ Questions for Class 9 Maths
- Number Systems Class 9 MCQ with Answers
- Polynomials Class 9 MCQ with Answers
- Coordinate Geometry Class 9 MCQ Questions
- Linear Equations in Two Variables Class 9 MCQ with Answers
- Lines and Angles Class 9 MCQ with Answers
- Triangles Class 9 MCQ with Answers
- Quadrilaterals Class 9 MCQ Questions
- Circles Class 9 MCQ with Answers
- Constructions Class 9 MCQ
- Heron’s Formula Class 9 MCQ with Answers
- Surface Area and Volume Class 9 MCQ
- Statistics Class 9 MCQ
- Probability Class 9 MCQ with Answers
Frequently Asked Questions on Polynomials Class 9 MCQ with Answers
1. Are these MCQ on Polynomials Class 9 are based on 2021-22 CBSE Syllabus?
Yes. There are 30 MCQ’s on this Chapter in this blog.
2. Are you giving all the chapters of Maths Class 9 MCQs with Answers which are given in CBSE syllabus for 2021-22 ?
Yes, we are providing all the chapters of Maths Class 9 MCQs with Answers.