S

10. Follow the steps provided to factor the polynomial completely: (30 points) f(x) =324 - 14x3 - 25x2 + 112x - 60 a. List the possible number of positive real zeros and negative real zeros. Positive : 3017 Negative : 1 b. List all of the possible rational zeros of the polynomial. 4 1 , 2 , 3 , 4, 5, 6, 10, 12, 15, 20, 30, 60 9 : + 1 .3 # 1 1 3, 21 3, 3, 4, 3, 513, 6, 10:3, 12, 15, 20,23, 30, 60 c. Use synthetic division to show that 2 is a zero of the polynomial. d. Use synthetic division to show that -3 is a zero. [Hint: Use the previous result] e. Use the division above to rewrite the polynomial as a product of quadratic and linear fac- tors. Then find the remaining zeros by solving the quadratic equation or using synthetic division. f. Write out the factored form of the polynomial