6.5 Day 1 Long Division, Remainder Theorem
Warm Up:
20 1156
For the below problems find the missing factor. Check your answer to make sure it is
correct.
1.) x 2 − 2 x − 63 = ( x − 9)(_______)
The degree of the _____________________ must be __________________ than the degree of the ________
Use LONG DIVISION of polynomials to divide the following:
1.) y 4 + 2 y 2 − y + 5 by y 2 − y + 1
2.) 2 x 4 + 3 x 3 + 5 x − 1 by x 2 − 2 x + 2
3.) (5 x 4 + 14 x 3 + 9 x) ÷ ( x 2 + 3 x)
6.5 Day 1 Long Division, Remainder Theorem
Example 1)
Let f ( x) = x 3 − x 2 − 2 x + 8
a.) Use long division to divide f ( x) by x + 2 . What is your remainder?
b.) Evaluate f (−2) for the above function. How does your answer relate to the
above question?
Remainder Theorem
If a polynomial ___________ is divided by ______________________, then the
remainder is _______________________________.
Use the remainder theorem to find the remainder of the division problem.
f ( x) = 3 x 3 − 2 x 2 + 2 x − 5 ÷ by x − 2
f ( x) = ( x 3 +2 x 2 − 6 x − 9) by ( x + 3)
Homework: pg. 356 #15-25 Odd
6.5 Day 1 Long Division, Remainder Theorem