Factorize the following polynomials- a)6x cube-x square-5x+2 b)x4+x3-7x2-x+6

Asked by raghavrattan | 10th Jul, 2010, 08:38: PM

Expert Answer:

Factorization of the above polynomials can be done as follows:
f(x) = 6x3-x2-5x+2
       Putting -1 in place of x gives f (x) = 0
       hence one root of f(x) becomes -1.
       and hence we can write :
f (x) = (x+1)(6x2-7x+2)
       = (x+1)(6x2-4x-3x+2)
       = (x+1)(2x(3x-2)-(3x-2)
       = (x+1)(3x-2)(2x-1)
b) f(x) = x4+x3-7x2-x+6
    f(1) = 0;
   this implies x = 1 is a root of f (x)
and hence we can write:
f(x) = (x-1)(x3+2x2-5x-6)
      = (x-1)g(x)
x = -1 is a root of g(x)
therefore we can write:
f(x) = (x-1)(x+1)(x2+x-6)
      = (x-1)(x+1)(x2+3x-2x-6)
      = (x-1)(x+1)(x+3)(x-2)

Answered by  | 13th Jul, 2010, 03:02: PM

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