Math Questions Polynomial Functions

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

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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.
4๐‘ฅ 3 + 6๐‘ฅ 2 โˆ’ 10๐‘ฅ + 4 รท 2๐‘ฅ โˆ’ 1
2. Divide using polynomial synthetic division.
3๐‘ฅ 3 + 5๐‘ฅ 2 โˆ’ 11๐‘ฅ + 3 รท ๐‘ฅ + 3
3. How many complex roots (zeros) does ๐‘“(๐‘ฅ) have shown below?
๐‘“(๐‘ฅ ) = โˆ’3๐‘ฅ 4 + 5๐‘ฅ โˆ’ 2
4. Using the polynomial listed below find the value that is ๐‘“(1).
๐‘“(๐‘ฅ ) = โˆ’2๐‘ฅ 3 + 5๐‘ฅ 2 โˆ’ 4๐‘ฅ + 8
5. Factor completely over the complex numbers for the polynomial listed
below. (Remember Iโ€™m not saying you need this much room, but Iโ€™m giving you this much
room just in case โ€“ I want you to show your work)
๐‘“(๐‘ฅ ) = ๐‘ฅ 3 โˆ’ 2๐‘ฅ 2 + 9๐‘ฅ โˆ’ 18
6. Factor the polynomial function listed below over the complex numbers.
๐‘“(๐‘ฅ ) = ๐‘ฅ 4 + 3๐‘ฅ 2 โˆ’ 4
7. Graph the polynomial function below. Make sure you identify your xintercepts, y-intercept, and 2 additional points as well as graph it.
๐‘“(๐‘ฅ ) = (๐‘ฅ + 3)(๐‘ฅ โˆ’ 1)(๐‘ฅ + 5)

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