Use the following function to answer parts a through c. 3 2 f(x)=x + 9x -213x-221 a. List all rational zeros that are possible according to the Rational Zero Theorem. (Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.) b. Use synthetic division to test several possible rational zeros in order to identify one actual zero. One rational zero of the given function is (Simplify your answer.) c. Use the zero from part (b) to find all the zeros of the polynomial function. The zeros of the function are (Simplify your answer. Use a comma to separate answers as needed. Type an integer or decimal rounded to three decimal places as needed.)

Use synthetic division to find the quotient and remainder when 0.2x° + 0.5x is divided by x+ 0.9 Quotient: (Use integers or decimals for any numbers in the expression. Round to the nearest thousandth as needed.) Remainder: (Round to four decimal places as needed.)

3. For the function f(x) = 2x4 – 5x3 + 9x² + x – 15: a. State the degree of the polynomial b. State the number of zeros the polynomial function will have. c. Use the Rational Zero Theorem to find all of the possible rational zeros d. Look at the graph or Table on a graphing calculator to determine which numbers on the list of rational zeros are real zeros indicated by the x-intercepts of the graph. In the space below, use synthetic division to verify one rational zero. Note: If the division remainder is zero, the number divided is a zero of the function. е. f. Find all remaining zeros. (Show work!) Note: Use the reduced polynomial (the quotient from the division) to continue the search for zeros © If the degree of the reduced polynomial is higher than 2, continue the synthetic division process with another real zero. (Remember: a number may be a multiple zero – i.e. occur more than once ) © Whenever the reduced polynomial is quadratic, the zeros can be found by using methods for…