MathematicsFactorize the polynomial expression x 2 −11x−42 , and choose the option which represents the factored form correctly.

Factorize the polynomial expression x 2 11x42 , and choose the option which represents the factored form correctly.


  1. A
      (x7)(x6)
  2. B
      (x14)(x+3)
  3. C
      (x+14)(x3)
  4. D
      None of these 

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    Solution:

    The given expression is as follows,
    x 2 11x42 .
    Now, to factorize the above expression further, we need to take the product of the first and last terms of the above expression, i.e.,
    x 2 ×(42)=42 x 2
    Next, we need to split middle term of the polynomial expression, i.e., 11x as a sum or difference of two terms, such that their product is equal to the product of first and last terms, i.e., 42 x 2 .
    x 2 11x42 x 2 14x+3x42
    Now, we need to group the terms and factor out the common factors, as follows,
    x 2 14x + 3x42 =x x14 +3 x14 = x14 x+3
    So, the factored form of the given polynomial expression is x14 x+3 .
    Hence, the correct option is (2).
     
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