find the complex zeros of each polynomial function. write f in factored form

Question

f(x) = x^3 - 8x^2 +25x-26

Answer 1

Step 1:

The function is .

Identify Rational Zeros.

Usually it is not possible to test all possible zeros of a polynomial function using only synthetic substitution.

The Rational Zero Theorem can be used for finding the some possible zeros for higher degree polynomial.

If   is a rational zero, then  is a factor of 26 and  is a factor of 1.

The possible values of are   ± 1, ± 2, ± 13 and  ± 26.

The possible values for are ± 1.

So, = ± 1,  ± 2, ± 13 and  ± 26.

Answer 2

Contd..

Step 2:

Make a table for the synthetic division and test possible  zeros.

Since ,  is one of the zero of the function.The depressed polynomial is .

The depressed polynomial, , is quadratic equation then the zeros of equation are calculated as.

Substitute , and in the above expression.

Therefore roots of are .

Answer 3

Contd..

Step 3:

Factor theorem,

When then   is a factor of polynomial.

Factors of the polynomial are then

Solution :

The Complex zeroes of the function are .

Factored form is .