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Polynomials Test - 17

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Polynomials Test - 17
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Weekly Quiz Competition
  • Question 1
    1 / -0
    Find the product of (6x2 + y) and (3x).
    Solution
    (6x2 + y) (3x) = 18x3 + 3xy
  • Question 2
    1 / -0
    Find the coefficient of y in the equation 4x2 - y - 6.
    Solution
    Coefficients are constant factors that multiply a variable or powers of a variable.
    So, coefficient of 'y' is -5/3.
  • Question 3
    1 / -0
    Find the value of 2a2b if a = 3 and b = 6.
    Solution
    a = 3 and b = 6
    2a2b
    = 2 x (3)2 x 6
    = 2 x 9 x 6
    = 108
  • Question 4
    1 / -0
    Which of the following is a trinomial?
    Solution
    (2x + 1)(2x + 1) = 4x2 + 4x + 1
    It is a trinomial, an algebraic expression having three terms.
  • Question 5
    1 / -0
    Find the difference between the following two expressions:

    2x2 + 3xy - 2xyz + 7y and x2 - 7xyz + xy
    Solution
    2x2 + 3xy - 2xyz + 7y - (x2 - 7xyz + xy)
    = 2x2 + 3xy - 2xyz + 7y - x2 + 7xyz – xy
    = (2x2 – x2) + (3xy – xy) + (- 2xyz + 7xyz) + 7y
    = x2 + 2xy + 5xyz + 7y
  • Question 6
    1 / -0
    The length of a rectangular field is ab + b2 and its width is 2b. Find the area of the field if a and b are both smaller than 1.
    Solution
    Area = Length x Width
    = (ab + b2)(2b) = 2ab2 + 2b3
  • Question 7
    1 / -0
    Find the perimeter of the square whose side is 3a2b, where a and b are both greater than 1.
    Solution
    Perimeter = 4 x Side
    = 4 x 3a2b
    = 12a2b
  • Question 8
    1 / -0
    There is a square playground whose side is 7ab2. What is the area of that playground if a, b > 1?
    Solution
    Area of the square playground = Side2 = (7ab2)2 = 49a2b4
  • Question 9
    1 / -0
    A rectangular field has length 5a2 + 2b and width 2a + b. Find its area.
    Solution
    Area of rectangular field = Length x Width
    = (5a2 + 2b) x (2a + b)
    = 5a2(2a + b) + 2b(2a + b)
    = 10a3 + 5a2b + 4ab + 2b2
  • Question 10
    1 / -0
    Find the area of a square with side 4a + 5b.
    Solution
    Area of square = (4a + 5b)2
    (a + b)2 = a2 + b2 + 2ab
    So, (4a + 5b)2 = (4a)2 + (5b)2 + 2(4a)(5b) = 16a2 + 25b2 + 40ab
  • Question 11
    1 / -0
    Which of the following are not like terms?
    Solution
    49a2bc2 and 56a2b2c2 are not like terms.
    Power of b is 1 in 49a2bc2 and 2 in 56 a2b2c2, which is not in other options.
    As in option 1, powers of a and b in both the terms are the same.
    Similarly, in options 2 and 3, these are the same.
    So, option 4 is the correct answer.
  • Question 12
    1 / -0
    Which of the following is the same as (a – 2b)2?
    Solution
    (a - b)2 = a2 + b2 - 2ab
    (a – 2b)2 = a2 + (2b)2 – 2a(2b) = a2 + 4b2 - 4ab
  • Question 13
    1 / -0
    Find the common factor of 24xy3z, 8 x2y2z2 and 28y6 z.
    Solution
    24xy3z = 2.2.2.3.x.y.y.y.z
    8 x2y2z2 = 2.2.2.x.x.y.y.z.z
    28y6z = 2.2.7.y.y.y.y.y.y.z

    Common factor     = 2.2.y.y.z = 4y2z
  • Question 14
    1 / -0
    Which of the following is the factorised form of x² + 2x − 8?
    Solution
    x² + 2x − 8 = x2 + 4x – 2x – 8 = x(x + 4) – 2(x + 4) = (x – 2)(x + 4)
  • Question 15
    1 / -0
    What will be the quotient if we divide (x2 - 9x - 10) by (x + 1)?
    Solution
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