1. 2.5 – Apply the remainder and factor theorems
Coach Bianco

2. Unit 2.5 – Apply the remainder and factor theorems
Georgia Performance Standards:
MM3A3c – Solve polynomial, exponential, and logarithmic inequalities analytically, graphically, and using appropriate technology. Represent solution sets of inequalities using interval notation.

3. Vocabulary
Polynomial long division – can be used to divide a polynomial f(x) by a divisor polynomial d(x), producing a quotient polynomial q(x) and a remainder polynomial r(x).
Synthetic division – can be used to divide any polynomial by a divisor of the form x – k.
Remainder Theorem – if a polynomial f(x) is divided by x – k, then the remainder is r = f(k).
Factor Theorem – a polynomial f(x) has a factor x – k, if and only if f(k) = 0.

4. Polynomial long division
Steps:
Set up like ANY long division problem you have done (Think 3rd grade!!)
Check for needed place holders (place holder = 0).
Multiply divisor to get first term
Always subtract – use parenthesis!!
Remainder goes over divisor at the end if you have one!

5. Polynomial long division
Divide f(x) = x2 + 3x + 6 by x + 1 using long division

6. Polynomial long division
Divide f(x) = x3 + 2 by x + 1 using long division

7. Try guided practice on page 86 (1 & 2)

8. Synthetic division Steps:
Use the opposite (If it’s positive make it negative, if it’s negative make it positive)
Set up your “L”
Remember to check for placeholders (Standard form!!)
Drop it!
Multiply it!
Add it!
Remainder goes over the divisor if you have one!

9. Synthetic division
Divide f(x) = x3 + 2 by x + 1 using synthetic division

10. Synthetic division
Divide f(x) = x4 + 2x3 – 5x2 + 3x -1 by x - 1 using synthetic division.

11. Try guided practice on page 86 (#4)