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?

Find all complex zeros of each polynomial function. Give exact values. List multiple zeros as necessary.* ƒ(x)=2x^4-x^3+7x^2-4x-4

Determine whether each statement is true or false. If false, explain why. For ƒ(x)=(x+2)^4(x-3), the number 2 is a zero of multiplicity 4.

In Exercises 1–8, use the Rational Zero Theorem to list all possible rational zeros for each given function. f(x)=4x^4−x^3+5x^2−2x−6

Use the factor theorem and synthetic division to determine whether the second polynomial is a factor of the first. See Example 1. x^3+6x^2-2x-7; x+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=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

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.