Please complete this assignment in its entirety, justifying your answers as you go. Using a method other than the requested method will not earn full credit. 1. List all of the possible rational roots of the polynomial p(x) = 3x5 + 2x\" 4x3 + 11x2 12. Do not solve. If 2 + 31' is a zero ofa polynomial function with real coefficients, what MUST be another root of the function? Why? Write a polynomial function with real coefficients, a scale factor of 1, and zeros x=~5 and x=3+ 4i in factored form. Then convert your answer to general form. (Hint: think about what you just answered in #2 to be sure you get all ofthe factors!) 4. Given 3 is a zero of p(x) = 2x3 - 3x1 - 29x + 60, find all zeros of p(x). Then write p(x) as a product of linear factors. Zeros: Factored form of p(x): 5. Given 5 4i is a zero of q(x)=3x' 29x3 + 111x2 + 61x82, find all zeros of q(x). Then write q(x) as a product of linearfactors. Zeros: Factored form of p(x): 6. Write each polynomial as a product of linear factors. a.y=5x32x220x+8 b.y=3x3+4x2+3x+4 c.y=x\"6x27 7. Find all complex solutions to each polynomial equation algebraically. (Do not use graphing technology.) Show all steps, including synthetic division you try (even if it doesn't work). (Hint: try factoring first! Three of them can be factored right away!) a.x3+x2=2x+2 b.x3=2x+x2 c.x5x\"7x3+7x2+ 12x12=0 d. 2x316x2+43x38=0 8. Use your results from 7a to solve the inequality x3 + x2 2x 2