MathematicsFind the coefficient of x2 in the following polynomial x+4x+4x+4.

Find the coefficient of x2 in the following polynomial x+4x+4x+4.


  1. A
    64
  2. B
    12
  3. C
    0
  4. D
    1 

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    Solution:

    The given polynomial isx+4x+4x+4.
    We know the formula,(a+b)3=a3+b3+3a2b+3ab2.
    Simplifying the given expression as,
    x+4x+4x+4=x+43
    Applying the formula in the above expression where a = x, b = 4, we get,
    (x+4)3=x3+43+3x2(4)+3(x)42
    (x+4)3=x3+64+12x2+48x
    We know that the coefficient of xm  in axm+bx+c is a.
    Therefore, coefficient of x2 in x3+64+12x2+48x is 12.
    Hence, option 2 is  correct.
     
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