2

Q1. If p(x) = 7 - 3x + 2x² then value of p(-2) is:

12

31

21

22

Q2. In the division of a cubic polynomial p(x) by a linear polynomial, the remainder is p(-2). So, the divisor must be

x - 2

x + 2

2x + 1

2x - 1  

Q3. If p(x) = 2x² - 3x + 1 does not have  x - a as a factor, then p(a) 

is equal to zero

is a non zero number

is 4a - 1

is 4a + 1

Q4. If (x - 2) is a factor of x² + 2x + a, find the value of 'a'.

a = -8

a = 8

a = -16

a = 16

Q5.   p(x) is a polynomial in x, ‘a’ is a real number. If (x - a) is a factor of p(x), then p(a) must be

positive

negative

zero

2a

Q6. What is the remainder when q(x) = 2x³ - x² + x - 1 is divided by x + 2?

20

- 23

35

- 32

Q7. Evaluate (11)³

1331

3113

1313

3131

Q8. Factorise the polynomial  x²ⁿ+ 5xⁿ + 6

(xⁿ- 3) (xⁿ- 2)

(xⁿ+ 3) (xⁿ- 2)

(xⁿ- 3)xⁿ+ 2)

(xⁿ+ 3)(xⁿ+ 2)

Q9. The degree of the polynomial x⁴ - 3x³ + 2x² - 5x + 3 is:

4

2

3

1

Q10. Find the coefficients of x² in x² - 2x + 4

- 2

2

1

-1

Q11. For a polynomial p(x) when divided by x + 3 leaves a remainder of 2. So, which of the following is true?

p(-3) = 2  

p(2) = -3  

p(3) = 2  

p(-2) = 3

Q12. Factorise: x⁷y + xy⁷

 xy(x² - y²)(x⁴ + y⁴ - x²y²) 

    xy(x² + y²)(x⁴ + y⁴ - x²y²)

    xy(x² + y²)(x⁴ - y² + x²y²)

    xy(x² - y²)(x⁴ - y⁴ + x²y²)

Q13. In 3z³ - 9x⁶ - 6y⁴ + z, the degree of the polynomial is 

1

3

4

6

Q14. Factorisation by splitting the middle term: 24x² - 65x + 21

 (3x + 7)( 8x - 3)

(3x - 7)( 8x - 3)

(3x - 7)( 8x+ 3)

(3x + 7)( 8x+ 3)

Q15. A linear polynomial will have how many zeroes.

1  

2

3

0

Q16. On dividing f(x) = 2x⁴ − 9x³ − 21x² + 88x + 48 by (x − 2), we get the remainder 

50

150

100

75

Q17. Evaluate 104³

1124864

1142846

1124844

1142864

Q18. Factorise: x⁴-1

   (x²+1)(x- 1) (x+1)

   (x²-1) (x-1)(x+1)

   (x²+1)(x- 1)(x-1)

   (x²+1) (x+1)(x+1)

Q19. Find the value of p such that (x - 1) is the factor of the polynomial x³ + 10x² + px.

p = 7

p = -7

p = -11

 p = 11

Q20. In 5y² + 8y - 3y³, 8 is the coefficient of 

y

y²

y³

y + 1

Q21. What is remainder when x³ - 2x² + x + 1 is divided by (x -1)?

0

-1

1

2

Q22. In −1x + 2y = z, what are the variables? 

−1, x, y

−1, 2, −1

x, y, z

−1, 2, 1

Q23.  Find the remainder when p(x) = x² - 2x is divided by x - 2.

1

0

- 1

2

Q24. The degree of a non-zero constant polynomial is always 

0

1

−1

2

Q25. 8x³ - 343y³ = ?

(2x-7y) (4x² + 14xy + 49y²)

(2x+7y)(4x² - 14xy + 49y²)

(2x + 7y) (2x - 7y)

(2x - 7y) (4x² - 49y²)

Q26. If 3a – 7b = 26 and ab = 5, then  the value of 9a² + 49b².

516

872

886

643

Q27. Factorise: x²- 81

    (x-9)(x-9)

    (x-9)(x+9)

    (x-81)(x+1)

    (x+9)(x+9)

Q28. For a polynomial p(x) = 2x⁴ - 3x³ + 2x² + 2x - 1, what is the remainder when it is divided by x + 4?

p(4)

p(-2)

p(- 4)

p(2)

Q29. Find the value of p(2) if p(x) has (x - 2) as its factor.

0

2

-2

3

Q30. If x - 2 is a factor of ax² - x - 6, then what should be the value of a?

3

 4

 2

 1

Q31. In y⁶ − 10y⁴ − 12y³ + 1, the coefficient of y³ is 

1

−10

−12

−1

Q32. One of the factors of (16y² - 1) + (1 - 4y)² is

(4 + y)

(4 - y)

(4y + 1)

8y

Q33. What is the remainder when x³ − 12x² − 42 is divided by x − 3? 

245

123

344

-123

Q34. The term mxⁿ… m is 

a natural number

a whole number

an integer

a real number

Q35. Degree of the polynomial p(x) = 4x⁴ + 2x³ + x⁵ + 2x + 7 is:

7

4

5

3

Q36. A linear polynomial is a polynomial of degree ……….

1  

2

0

3

Q37. Evaluate: (102)²

  10444

  10404

  10044

10440

Q38. What is the coefficient of x in x³ + 3x² - 2x - 1?

-2

1  

3  

-1  

Q39. Find the value of (12m – 15n) ²

122m² – 360mn + 225n²

144m² – 180mn + 225n²

144m² – 360mn + 225n²

144m² + 360mn + 125n²

Q40. Factorize: 125a³ – 27b³ – 225a²b + 135ab².

(5a + 3b) (5a – 3b) (5a + 9b)

(3a – 5b) (3a – 5b) (3a – 5b)

(5a – 3b) (5a – 3b) (5a – 3b)

(3a – 5b) (5a – 3b) (3a + 5b) ²

Solution