1. 1 Algebra 2: Section 6.5 The Remainder and Factor Theorems (Day 1)

2. 2 Remember from 4 th Grade…… Steps: –D–D–D–Divide –M–M–M–Multiply –S–S–S–Subtract –B–B–B–Bring Down Start over again –H–H–H–How to write the remainder…..

3. 3 Polynomial Long Division Same format as long division for numbers Use a coefficient of zero for any ‘missing’ powers of the variable At each stage ask, “What do I multiply the first term of the divisor by to get the leading term?” (  goes above matching power) Add the remainder divided by the divisor to the answer.

4. Examples 4 Remainder

5. 5 Examples

6. 6

7. 7 Remainder Theorem Using Synthetic Substitution!!! If a polynomial is divided by x - k, then the remainder is f(k) –f(k) = answer x – 3x + 2 x – 3x + 2 x + 4x - 5  Don’t forget to look for missing powers of “x”!

8. 8 Examples Remainder

9. 9 Homework p.356 #16-38 evens Look at #22 and # 24 (keep 0x even under the bottom) What is 0x times x?