MathematicsFactorize  2×2+35x+5 by splitting the middle term.

Factorize  2x2+35x+5 by splitting the middle term.


  1. A
    2x+5x-5
  2. B
    (2x-5)(x+5)
  3. C
    (2x+5)(x+5)
  4. D
    (2x-5)(x-5) 

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    Solution:

    The given polynomial is 2x2+35x+5.
    Comparing the given polynomial with ax2+bx+c we get,
    where, a=2,b=35,c=5 .
    Here ac=25=10  , so we try to split b= 35  into two parts whose sum is 35and the product is 10.
    Therefore, possible factors are 25and5, -25and-5.
    Clearly, pair 25and5 gives 25+5=35=b.
    =2x2+(25+5)x+5
    =2x2+25x+5x+5
    =2x(x+5)+5(x+5)
    =(2x+5)(x+5) Thus, the factors of 2x2+35x+5 , by using splitting the middle term are (2x+5)(x+5).
    Therefore, option 3 is correct.
     
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