MathematicsFactorize the following by using splitting the middle term x2+2x-3 .

Factorize the following by using splitting the middle term x2+2x-3 .


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

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    Solution:

    The given polynomial is x2+2x-3.
    Comparing the given polynomial with ax2+bx+c we get,
    f(x)= x2+2x-3  where, a=1,b=2,c=-3.
    Here =(1)(-3)=-3 , so we try to split b=2 into two parts whose sum is 2 and product is -3.
    Therefore, possible factors are -3 and 1, 1 and -3.
    Clearly, pair -1 and 3 gives -1+3=2=b.
    =x2+-1+3x-3 =x2-x+3x-3  =x(x-1)+3(x-1)  =(x-1)(x+3) Thus, the factors of x2+2x-3 , by using splitting the middle term are (x-1)(x+3) .
    Therefore, option 2 is correct.
     
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