Page No 32:
Question 1:
Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.
(i)  (ii)  (iii)
(iv)  (v) 

Page No 32:
Question 2:
Write the coefficients of in each of the following:
(i)  (ii) 
(iii)  (iv) 

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Question 4:
Write the degree of each of the following polynomials:
(i)  (ii) 
(iii)  (iv) 3

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Question 5:
Classify the following as linear, quadratic and cubic polynomial:
(i) (ii)  (iii)  (iv)  (v) 
(vi)  (vii) 

Page No 34:
Question 1:
Find the value of the polynomial  at
(i) x = 0 (ii) x = −1 (iii) x = 2

Page No 34:
Question 2:
Find p(0), p(1) and p(2) for each of the following polynomials:
(i) p(y) = y² − y + 1 (ii) p(t) = 2 + t + 2t² − t³
(iii) p(x) = x³ (iv) p(x) = (x − 1) (x + 1)

Page No 35:
Question 4:
Find the zero of the polynomial in each of the following cases:
(i) p(x) = x + 5 (ii) p(x) = x − 5 (iii) p(x) = 2x + 5
(iv) p(x) = 3x − 2 (v) p(x) = 3x (vi) p(x) = ax, a ≠ 0
(vii) p(x) = cx + d, c ≠ 0, c, are real numbers.

Page No 40:
Question 1:
Find the remainder when x³ + 3x² + 3x + 1 is divided by
(i) x + 1 (ii)  (iii) x
(iv) x + π (v) 5 + 2x

Page No 43:
Question 1:
Determine which of the following polynomials has (x + 1) a factor:
(i) x³ + x² + x + 1 (ii) x⁴ + x³ + x² + x + 1
(iii) x⁴ + 3x³ + 3x² + x + 1 (iv) 

Page No 43:
Question 2:
Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases:
(i) p(x) = 2x³ + x² − 2x − 1, g(x) = x + 1
(ii) p(x) = x³ + 3x² + 3x + 1, g(x) = x + 2
(iii) p(x) = x³ − 4 x² + x + 6, g(x) = x − 3

Page No 44:
Question 3:
Find the value of k, if x − 1 is a factor of p(x) in each of the following cases:
(i) p(x) = x² + x + k (ii) 
(iii)  (iv) p(x) = kx² − 3x + k

Page No 44:
Question 4:
Factorise:
(i) 12x² − 7x + 1 (ii) 2x² + 7x + 3
(iii) 6x² + 5x − 6 (iv) 3x² − x − 4

Page No 44:
Question 5:
Factorise:
(i) x³ − 2x² − x + 2 (ii) x³ + 3x² −9x − 5
(iii) x³ + 13x² + 32x + 20 (iv) 2y³ + y² − 2y − 1

Page No 48:
Question 1:
Use suitable identities to find the following products:
(i)  (ii) 
(iii)  (iv) 
(v) 

Page No 48:
Question 2:
Evaluate the following products without multiplying directly:
(i) 103 × 107 (ii) 95 × 96 (iii) 104 × 96

Page No 48:
Question 3:
Factorise the following using appropriate identities:
(i) 9x² + 6xy + y²
(ii) 
(iii) 

Page No 49:
Question 4:
Expand each of the following, using suitable identities:
(i)  (ii) 
(iii)  (iv) 
(v)  (vi) 

Page No 49:
Question 5:
Factorise:
(i) 
(ii) 

Page No 49:
Question 6:
Write the following cubes in expanded form:
(i)  (ii) 
(iii)  (iv) 

Page No 49:
Question 7:
Evaluate the following using suitable identities:
(i) (99)³ (ii) (102)³ (iii) (998)³

Page No 49:
Question 8:
Factorise each of the following:
(i)  (ii) 
(iii)  (iv) 
(v) 

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Question 9:
Verify:
(i) 
(ii) 

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Question 10:
Factorise each of the following:
(i) 
(ii) 

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Question 11:
Factorise: 

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Question 12:
Verify that 

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Question 13:
If x + y + z = 0, show that x³ + y³ + z³ = 3xyz

Page No 49:
Question 14:
Without actually calculating the cubes, find the value of each of the following:
(i) 
(ii) 

Page No 49:
Question 15:
Give possible expressions for the length and breadth of each of thefollowing rectangles, in which their areas are given:

Page No 50:
Question 16:
What are the possible expressions for the dimensions of the cuboids whose volumes are given below?