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.
Answer:
Explanation:
We can factor the numerator and denominator as;
(
x
−
2
)
(
x
−
1
)
2
x
(
x
−
1
)
We can now cancel common term in the numerator and denominator:
(
x
−
2
)
(
x
−
1
)
2
x
(
x
−
1
)
⇒
x
−
2
2
x
However, we cannot divide by
0
so we must exclude:
2
x
=
0
⇒
x
=
0
and
x
−
1
=
0
⇒
x
1
x
2
−
3
x
+
2
2
x
2
−
2
x
=
x
−
2
2
x
Where:
x
≠
0
and
x
≠
1
Or
x
2
−
3
x
+
2
2
x
2
−
2
x
=
x
2
x
−
2
2
x
=
1
2
−
1
x
Where:
x
≠
0
and
x
≠
1
Step-by-step explanation: