Assignment 19 (2A.3.2) - Math with Mr.Kwongmrkwongckm.weebly.com/.../assignment_19__2a.3.2_.pdf · Assignment 19 (2A.3.2) The Remainder Theorem Homework: Pg.77 (1-10) & Read 78-80

Assignment 19 (2A.3.2) The Remainder Theorem Homework: Pg.77 (1-10) & Read 78-80

Warm Up Determine the end behaviors of the polynomials with the following leading coefficients. 𝑥!, 𝑥!,−𝑥!,−𝑥!, 𝑥!,−𝑥!, 𝑥!,−𝑥! Notes Partner Investigation: Which of the following are factors of 40? 8, 3, 12, 5

(Explain how) Dividing polynomials by Synthetic Division

When the polynomial 𝑓(𝑥) is divided by (𝑥 − 𝑐) c (coefficients of 𝑓(𝑥) )

1) Drop 2) Multiply 3) Bring up and Add The Remainder Theorem If the polynomial 𝑓(𝑥) is divided by 𝑥 − 𝑐, then the remainder is 𝑓 𝑐 .

The Factor Theorem If 𝑓 𝑐 = 0, then 𝑥 − 𝑐 is a factor of 𝑓 𝑥  . (𝑥 − 𝑐)  is a factor of 𝑓(𝑥) if the remainder is zero

Ex.1) Divide using synthetic division a. (3𝑥! + 17𝑥! + 21𝑥 − 9) ÷ (𝑥 + 3) b. (𝑥! − 2𝑥! + 3𝑥 − 5) ÷ (𝑥 − 1) c. (𝑥! − 4𝑥! + 5𝑥 + 3) ÷ (𝑥 − 2) Ex.2) Use the remainder theorem to evaluate a. 𝑓 𝑥 = 9𝑥! − 18𝑥! − 𝑥 + 2; 𝑓(−2) b. 𝑓 𝑥 = 2𝑥! − 3𝑥! + 5𝑥! − 𝑥 + 4; 𝑓(3) Workbook 2A.3.2 (1-10)