Questions: a) Find the rational zeros and then the other zeros of the polynomial function (f(x)=x^3-17 x^2+55 x+25), that is, solve (f(x)=0). b) Factor (f(x)) into linear factors. a) Select the correct choice below and fill in the answer box within your choice. (Type an exact answer, using radicals as needed. Simplify your answer. Use a comma to separate answers as needed.) A. There are only rational zeros and they are . B. There are no rational zeros. The other zeros are . C. The rational zero(s) is/are , and the other zero(s) is/are .

a) Find the rational zeros and then the other zeros of the polynomial function (f(x)=x^3-17 x^2+55 x+25), that is, solve (f(x)=0).
b) Factor (f(x)) into linear factors.
a) Select the correct choice below and fill in the answer box within your choice.
(Type an exact answer, using radicals as needed. Simplify your answer. Use a comma to separate answers as needed.)
A. There are only rational zeros and they are .
B. There are no rational zeros. The other zeros are .
C. The rational zero(s) is/are , and the other zero(s) is/are .

Transcript text: a) Find the rational zeros and then the other zeros of the polynomial function $f(x)=x^{3}-17 x^{2}+55 x+25$, that is, solve $f(x)=0$. b) Factor $f(x)$ into linear factors. a) Select the correct choice below and fill in the answer box within your choice. (Type an exact answer, using radicals as needed. Simplify your answer. Use a comma to separate answers as needed.) A. There are only rational zeros and they are $\square$ . B. There are no rational zeros. The other zeros are $\square$ . C. The rational zero(s) is/are $\square$ , and the other zero(s) is/are $\square$ .

Solution

Solution Steps

Step 1: Finding Rational Zeros

Using the Rational Root Theorem, the possible rational zeros are {1, 5, -25, 25, -5, -1}. After testing, the actual rational zeros are [5].

Step 2: Finding Other Zeros

After factoring out the rational zeros, the remaining polynomial is 1_x^2 - 12_x - 5. Solving this polynomial gives the other zeros: [(-0.403+0j), (12.403+0j)]

Step 3: Factoring into Linear Factors

The polynomial can be factored into linear factors as: (x - (5)) * (x - ((-0.403+0j))) * (x - ((12.403+0j)))