Solve the equation $x^{3}-13 x^{2}+47 x-35=0$ given that 1 is a zero of $f(x)=x^{3}-13 x^{2}+47 x-35$
The solution set is (Use a comma to separate answers as needed.)
Answer
Final Answer: The solution set is \(\boxed{1, 7, 5}\).
Step 1 ：Given that 1 is a zero of the function, we can use synthetic division to find the other zeros. Synthetic division is a shorthand method of dividing a polynomial by a linear binomial by using only the coefficients. The coefficients of the polynomial are 1, -13, 47, and -35. We will use synthetic division to divide these coefficients by (x - 1), which corresponds to the zero of 1.
Step 2 ：The roots of the resulting polynomial are 7 and 5. Therefore, the solutions to the original equation are 1, 7, and 5.
Step 3 ：Final Answer: The solution set is \(\boxed{1, 7, 5}\).
