Exercises 82–84 will help you prepare for the material covered in the next section. Let f(x)=an(x⁴−3x²−4). If f(3)=−150, determine the value of a_n.

Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. $\text{ƒ}\left(x\right)=3x^4+2x^3-8x^2-10x-1$

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)=4x³+3x²+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.

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