In Exercises 1–8, use the Rational Zero Theorem to list all possible rational zeros for each given function. f(x)=3x^4−11x^3−3x^2−6x+8

Find all zeros of f(x) = x³ + 5x² – 8x + 2.

Find all complex zeros of each polynomial function. Give exact values. List multiple zeros as necessary.* ƒ(x)=5x^3-9x^2+28x+6

Find all complex zeros of each polynomial function. Give exact values. List multiple zeros as necessary.* ƒ(x)=4x^3+3x^2+8x+6

Determine whether each statement is true or false. If false, explain why. A polynomial function having degree 6 and only real coefficients may have no real zeros.

Use the factor theorem and synthetic division to determine whether the second polynomial is a factor of the first. See Example 1. 4x^2+2x+54; x-4

Use the factor theorem and synthetic division to determine whether the second polynomial is a factor of the first. See Example 1. x^3+2x^2+3; x-1

Factor ƒ(x) into linear factors given that k is a zero. See Example 2. ƒ(x)=2x^3-3x^2-5x+6; k=1

In Exercises 25–32, find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing utility, use it to graph the function and verify the real zeros and the given function value. n=4; -2, 5, and 3+2i are zeros; f(1) = -96