Answer:

Explanation:
Given polynomial function:

Each answer option has (x - 1) as a factor.
Therefore, (x - 1) must be a factor of the given polynomial.
To double-check this, we can use the Factor Theorem.
The Factor Theorem states that if f(x) is a polynomial, and f(a) = 0, then (x - a) is a factor of f(x).
Therefore, if (x - 1) is a factor of f(x), then we would expect f(1) = 0:

Therefore, this confirms that (x - 1) is a factor of the given polynomial.
Divide the polynomial by the found linear factor using the method of long division:

Therefore:

Factor out 2 from the quadratic factor:

Factor the quadratic:

Therefore, the fully factored polynomial is:

Rearrange the factors to give:
