2. Polynomials Class 9 Mathematics NCERT Exemplar Solutions (CBSE)
Chapter 2: Polynomials – Class 9 Mathematics NCERT Exemplar Solutions (CBSE Board)
Chapter 2: Polynomials
EXERCISE 2.1
Write the correct answer in each of the following :
1. Which one of the following is a polynomial?
(A) x²2-2x²
(B) 2x-1
(C) x²+3x32x
(D) x-1x+1
2. 2
is a polynomial of degree
(A) 2 (B) 0 (C) 1 (D) 12
3. Degree of the polynomial 4x4+0x3+0x5+5x+7
is
(A) 4 (B) 5 (C) 3 (D) 7
4. Degree of the zero polynomial is
(A) 0 (B) 1 (C) Any natural number (D) Not defined
5. If x=x²-22+1
, then p22
is equal to
(A) 0 (B) 1 (C) 42
(D) 82+1
6. The value of the polynomial 5x–4x²+3
, when x=–1
is
(A) – 6 (B) 6 (C) 2 (D) –2
7. If p(x) = x + 3
, then p(x) + p(–x)
is equal to
(A) 3 (B) 2x
(C) 0 (D) 6
8. Zero of the zero polynomial is
(A) 0 (B) 1
(C) Any real number (D) Not defined
9. Zero of the polynomial p(x) = 2x + 5
is
(A) -25
(B) -52
(C) 25
(D) 52
10. One of the zeroes of the polynomial 2x²+7x–4
is
(A) 2 (B) 12 (C) -12
(D) –2
11. If x51+51
is divided by x + 1
, the remainder is
(A) 0 (B) 1 (C) 49 (D) 50
12. If x + 1 is a factor of the polynomial 2x²+kx,
then the value of k is
(A) –3 (B) 4 (C) 2 (D) –2
13. x + 1 is a factor of the polynomial
(A) x³ + x² – x + 1
(B) x³+ x²+ x + 1
(C) x4+ x² + x² + 1
(D) x4+ 3x³+ 3x²+ x + 1
14. One of the factors of (25x² – 1) +(1+5x)2 
is
(A) 5 + x
(B) 5 – x
(C) 5x – 1
(D) 10x
15. The value of 249² – 248²
is
(A) 1 2 (B) 477 (C) 487 (D) 497
16. The factorisation of 4x²+ 8x + 3
is
(A) (x + 1) (x + 3)
(B) (2x + 1) (2x + 3)
(C) (2x + 2) (2x + 5)
(D) (2x –1) (2x –3)
17. Which of the following is a factor of (x+y)3-(x3+y3)
?
(A) x²+y²+2xy
(B) x²+y²–xy
(C) xy²
(D) 3xy
18. The coefficient of x in the expansion of (x+3)3
is
(A) 1 (B) 9 (C) 18 (D) 27
19. If xy+yx=-1
, (x , y ≠0)
, the value of x³–y³
is
(A) 1 (B) –1 (C) 0 (D) 12
20. If 49x²-b=7x+127x-12
then the value of b is
(A) 0 (B) 12
(C) 14
(D) 12
21. If a + b + c = 0
, then a³+b³+c³
is equal to
(A) 0 (B) abc
(C) 3abc
(D) 2abc
Exercise 2.3
8. If px=x2-4x+3 
,evaluate : p2-p-1+p12
12. Find the zeroes of the polynomial : px=(x-2)2-(x+2)2
22. If x+1
is a factor of ax3+x2-2x+4a-9
, find the value of a
.
1. If the polynomials az³+4z²+3z-4
and z³-4z+a
leave the same remainder
when divided by z – 3
, find the value of a
.
2. The polynomial px= x4-2x³+3x²-ax+3a-7
when divided by x+1 leaves
the remainder 19. Find the values of . Also find the remainder when p(x)
is divided by +2
.
3. If both x–2
and x-12
are factors of x²+5x+r
, show that p=r
.
7. If a, b, c
are all non-zero and +b+c=0
, prove that a²bc+b²ca+c²ab=3
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