The remainder theorem is " If a polynomial f(x) is divided by , the remainder is r = f(k) ".

The factor theorem is " A polynomial f(x) has a factor ".

The polynomial function and factors .

By using remainder theorem and by using factor theorem is a factor of f(x).

By using remainder theorem and by using factor theorem is a factor of f(x).

So, are factors of the polynomial f(x).

The given factors are factors of the polynomial f(x).

The remainder theorem is " If a polynomial f(x) is divided by , the remainder is r = f(k) ".

The factor theorem is " A polynomial f(x) has a factor ".

The polynomial function and factors .

By using remainder theorem and by using factor theorem is a factor of f(x).

By the resulting quadratic expression factor as

The complete factorization of f(x) is .

The remaining  factor of polynomial f(x) is .