Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. $\text{ƒ}\left(x\right)=4x^3-x^2+2x-7$

Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. $\text{ƒ}\left(x\right)=6x^4+2x^3+9x^2+x+5$

Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. $\text{ƒ}\left(x\right)=5x^6-6x^5+7x^3-4x^2+x+2$

Find all complex zeros of each polynomial function. Give exact values. List multiple zeros as necessary. $\text{ƒ}\left(x\right)=x^4+x^3-9x^2+11x-4$

Use the Rational Zero Theorem to list all possible rational zeros for each given function. f(x)=x³+x²−4x−4

Determine whether each statement is true or false. If false, explain why. The product of a complex number and its conjugate is always a real number.

In Exercises 9–16, a) List all possible rational zeros. b) Use synthetic division to test the possible rational zeros and find an actual zero. c) Use the quotient from part (b) to find the remaining zeros of the polynomial function. f(x)=x³+x²−4x−4

In Exercises 9–16, a) List all possible rational zeros. b) Use synthetic division to test the possible rational zeros and find an actual zero. c) Use the quotient from part (b) to find the remaining zeros of the polynomial function. f(x)=x³−2x²−11x+12