Solve each problem. Use Descartes' rule of signs to determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of ƒ(x)=x^3+3x^2-4x-2.

If ƒ(x) is a polynomial function with real coefficients, and if 7+2i is a zero of the function, then what other complex number must also be a zero?

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=3; -5 and 4+3i are zeros; f(2) = 91

Show that each polynomial function has a real zero as described in parts (a) and (b). In Exercises 31 and 32, also work part (c). ƒ(x)=6x^4+13x^3-11x^2-3x+5no zero less than -3

For each polynomial function, one zero is given. Find all other zeros. See Examples 2 and 6. ƒ(x)=x^3-x^2-4x-6; 3

In Exercises 35–36, use the Rational Zero Theorem to list all possible rational zeros for each given function. f(x) = x^4 - 6x^3 + 14x^2 -14x + 5

In Exercises 39–52, find all zeros of the polynomial function or solve the given polynomial equation. Use the Rational Zero Theorem, Descartes's Rule of Signs, and possibly the graph of the polynomial function shown by a graphing utility as an aid in obtaining the first zero or the first root. f(x)=3x^4−11x^3−x^2+19x+6

In Exercises 49–50, find all the zeros of each polynomial function and write the polynomial as a product of linear factors. f(x) = 2x^4 + 3x^3 + 3x - 2

For each polynomial function, find all zeros and their multiplicities. ƒ(x)=3x(x-2)(x+3)(x^2-1)