PreCalculus 4.1: Polynomial Division Assignment 46 𝐫𝐞𝐦𝐚𝐢𝐧𝐝𝐞𝐫
Use synthetic division to divide. Write the answer as quotient + 𝐝𝐢𝐯𝐢𝐬𝐨𝐫 . Remember to use placeholders. 1. 2. 3. 4. Use regular polynomial division to divide. Remember that synthetic division cannot be used when the divisor is non-­‐linear. 5. 6. Write a polynomial function in factored form and standard form given the following known zeros and degree. a. b. c. 7. Use synthetic division to determine if the given binomial is a factor of the polynomial. 8. Use the given zero and synthetic division to write the polynomial in completely factored form. a. b. c. Answers: 1. 𝑥 ! + 4𝑥 − 4 +
!!
!!!
2. 3𝑥 ! + 3𝑥 − 5 +
7
𝑥−1
3. 𝑥 ! − 3𝑥 + 9 4. 𝑥 ! + 5𝑥 ! + 10𝑥 + 4 5. 𝑥 + 1 +
!!!!
! ! !!
6. b. 𝑃 𝑥 = (𝑥 + 2)(𝑥 + 3)(𝑥 − 3) 𝑃 𝑥 = 𝑥 ! + 2𝑥 ! − 3𝑥 − 6 7. a. yes b. yes 8. a. 𝑃 𝑥 = 𝑥 − 2 𝑥 + 1 𝑥 + 3 b. 𝑃 𝑥 = 𝑥 − 2 𝑥 − 1 𝑥 + 3 c. 𝑃 𝑥 = 𝑥 + 2 3𝑥 − 2 3𝑥 + 2