MathematicsFactorize  3×2+7x-6 by splitting the middle term.

Factorize  3x2+7x-6 by splitting the middle term.


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

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    Solution:

    The given polynomial is 3x2+7x-6.
    Comparing the given polynomial with ax2+bx+c we get,
    a=3,b=7,c=-6 .
    Here ac=(3)(-6)=-18  , so we try to split b=7 into two parts whose sum is 7 and product is -18.
    Therefore, possible factors are -9 and 2, -2 and 9.
    Clearly, pair -2 and 9 gives -2+9=7=b
    =3x2+(-2+9)x-6
    =3x2-2x+9x-6
    =3x(x+3)-2(x+3)
    =(3x-2)(x+3) Thus, the factors of 3x2+7x-6 , by using splitting the middle term are (3x-2)(x+3).
    Therefore, option 2 is correct.
     
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