Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. $\text{ƒ}\left(x\right)=2x^5-7x^3+6x+8$

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)=5x³-9x²+28x+6

Find all complex zeros of each polynomial function. Give exact values. List multiple zeros as necessary.* ƒ(x)=4x³+3x²+8x+6

In Exercises 1–8, use the Rational Zero Theorem to list all possible rational zeros for each given function. f(x)=3x⁴−11x³−3x²−6x+8

Use the factor theorem and synthetic division to determine whether the second polynomial is a factor of the first. 4x²+2x+54; x-4

Use the factor theorem and synthetic division to determine whether the second polynomial is a factor of the first. x³+2x²+3; x-1

Factor ƒ(x) into linear factors given that k is a zero. $\text{ƒ}\left(x\right)=2x^3-3x^2-5x+6{;}^{}k=1$