The following function is given. f(x) = x° - 3x² - 25x + 75 a. List all rational zeros that are possible according to the Rational Zero Theorem. (Use a comma to separate answers as needed.) 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 f(x) = x° - 3x2 - 25x + 75 are (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed.)

Please show work and explain

Please help me answer this question.

Find all the real zeros of the following polynomial. f(x) = x* – 729x . Enter your answer(s) as ordered pairs separated by a comma, (x, y).

Pls read and help2

Need help with a, b, and c.

Consider f (x) = 2x* – x3 – 5x2 + 2x + 2. 1. List all possible zeros (candidates) for f(x). 2. Define f (x) in your calculator or desmos. Use the graph to narrow down your candidates. Use synthetic division to reduce f (x) to a quadratic expression. Factor the resulting quadratic expression to find the last two zeros. ZEROS: 3. Express f(x) as a product of linear factors. Don't forget to include the value of a!

3. Let f(x) = 3x* – 4x³ – 14x² – 4x + 3. (a.) Use the Rational Zero Theorem to list out the possible rational zeros of f. (b.) Use part (a.) along with synthetic division and factoring to find all zeros of f. Write the complete factorization for f(x). (c.) Sketch the graph of f. Make sure your graph shows the x-intercepts and exhibits proper end behavior.

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…

Please help me