Math Questions Polynomial Functions

Please answer these questions like the way you did the other questions from a couple weeks ago

Directions: Show all necessary work to complete the problems listed below.
Remember I need to see your work to give you maximum amount of credit earned.
1. Divide using polynomial long division.
4𝑥 3 + 6𝑥 2 − 10𝑥 + 4 ÷ 2𝑥 − 1
2. Divide using polynomial synthetic division.
3𝑥 3 + 5𝑥 2 − 11𝑥 + 3 ÷ 𝑥 + 3
3. How many complex roots (zeros) does 𝑓(𝑥) have shown below?
𝑓(𝑥 ) = −3𝑥 4 + 5𝑥 − 2
4. Using the polynomial listed below find the value that is 𝑓(1).
𝑓(𝑥 ) = −2𝑥 3 + 5𝑥 2 − 4𝑥 + 8
5. Factor completely over the complex numbers for the polynomial listed
below. (Remember I’m not saying you need this much room, but I’m giving you this much
room just in case – I want you to show your work)
𝑓(𝑥 ) = 𝑥 3 − 2𝑥 2 + 9𝑥 − 18
6. Factor the polynomial function listed below over the complex numbers.
𝑓(𝑥 ) = 𝑥 4 + 3𝑥 2 − 4
7. Graph the polynomial function below. Make sure you identify your xintercepts, y-intercept, and 2 additional points as well as graph it.
𝑓(𝑥 ) = (𝑥 + 3)(𝑥 − 1)(𝑥 + 5)