Mathematics‘(x-1) is a factor of 4×3+3×2-4x-3’.State true or false.

'(x-1) is a factor of 4x3+3x2-4x-3’.


State true or false.


  1. A
    true
  2. B
    false 

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    Solution:

    The given expression is 4x3+3x2-4x-3.
    We know that the factor theorem states, if f(x) is a polynomial of degree n1 and a be a real number,then (x-a) is a factor of f(x) , if f(a)=0.
    Let (x-1) is the factor of a given polynomial.
     (x-1)=0 
    x=1
    Checking whether the value of x satisfies the given polynomial or not.
    Therefore, substituting the values of x in the given polynomial, we get,
    At x=1,
    f2=413+3(1)2-42-3
    =4+3-4-3
    f1=0
    Clearly, this value of x satisfies the given polynomial.
    Hence, (x-1) is the factor of a given polynomial.
    Therefore, the given statement is true i.e, '(x-1) is a factor of 4x3+3x2-4x-3.
    Hence, option 1 is  correct.
     
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