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Polynomials Test - 10

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Polynomials Test - 10
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Weekly Quiz Competition
  • Question 1
    1 / -0

    If x + y = 4 and xy = 2, then what is the value of x2 + y2?

    Solution

    x + y = 4 and xy = 2
    (x + y)2 = x2 + y2 + 2xy
    (4)2 = x2 + y2 + 2(2)
    x2 + y2 = 16 - 4 = 12

     

  • Question 2
    1 / -0

    Find the missing term (blank) in the following equation:

    2x2y + 4xz + 6xy = ____ (xy + 2z + 3y)

    Solution

    2x2y + 4xz + 6xy
    = 2x(xy + 2z + 3y)

     

  • Question 3
    1 / -0

    What is the value of (2x + 3y)– (2x)2?

    Solution

    (2x + 3y)2 – (2x)2
    We know that a2 – b2 = (a + b) (a – b).
    ∴ (2x + 3y)2 – (2x)2 = (2x + 3y + 2x)(2x + 3y – 2x)
    = (4x + 3y)(3y)

     

  • Question 4
    1 / -0

    If (104)2 = 10000 + A2 + 200A, then what is the value of A?

    Solution

    (104)2 = (100 + 4)2
    Using (a + b)2 = a2 + b+ 2ab, we get
    (100 + 4)2 = 10000 + 42 + 200(4)
    ∴ A = 4

     

  • Question 5
    1 / -0

    What is the result of [(2x - 6)(2x - 5) + (x + 6)(x - 5)]?

    Solution

    We know,
    (x + a)(x + b) = x2 + (a + b)x + ab
    (2x - 6)(2x - 5) = (2x)2 + (-6 - 5)2x + (-6)(-5)

    = 4x2 - 22x + 30 ... (i)
    (x + 6)(x - 5) = x2 + (6 -5)x + (6)(-5)

    = x2 + x - 30 ... (ii)
    Now, on adding (i) and (ii), we get

    x2 + x - 30 + 4x2 - 22x + 30
    = 5x2 - 21x

     

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