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Answer: The factor form of the function F(x) is , where
gives two complex roots.
Explanation:
The given function is,
According to the rational root theorem 1 and -1 are the possible roots of each polynomial.
Put x=-1
Since the value of F(x) is 0 at x=-1 therefore the -1 is a root of given polynomial and (x+1) is a factor of F(x).
Use synthetic division method to divide the polynomial by (x+1).
The last row of the synthetic division shows the coefficient of remaining polynomial.
At x=2 the value of F(x) is 0, therefore (x-2) is a factor of F(x).
Use synthetic division method to divide the polynomial by (x-2).
Therefore the roots of F(x) are,
Where factors with real root and
are factors with complex roots.
