1. Bell Ringer
In elementary school, you learned long division. Describe, in detail, how to divide 230 by 4 without a calculator.

2. Dividing Polynomials
Wednesday, March 6, 2019

3. Polynomials? Mono- is a prefix meaning “one”
What are
Mono- is a prefix meaning “one”
Bi- is a prefix meaning “two”
Tri- is a prefix meaning “three”
Poly- is a prefix meaning “many”
-nomial is a suffix meaning “terms”
Polynomial = Many Terms
Polynomials?

4. How do we work with
We can perform operations with polynomials (addition, subtraction, multiplication, and division).
When we write polynomials, the standard is to write in descending order of the exponents.
The degree of a polynomial is the highest exponent or sum of the exponents if there are multiple variables in the same term.
Polynomials?

5. Review – Adding, Subtracting, & Multiplying
Adding – Combine Like Terms
Subtracting – Add the Opposite
Subtracting Polynomials
Adding Polynomials
(a3 – 2a2) – (3a2 – 4a3)
Add the opposite, so…
(a3 – 2a2) + (-3a2 + 4a3)
Combine like terms… a3 + 4a3 = 5a a2 + -3a2 = -5a2
5a3 – 5a2
(5p2 -3) + (2p2 – 3p3)
Identify like terms and combine them p2 + 2p2 = 7p2
Write in descending order of the exponents.
-3p3 + 7p2 -3

6. Review – Adding, Subtracting, & Multiplying
Multiplying – Multiply the Constants, then the Variables – DISTRIBUTE!!!
Examples:
binomial by a binomial
monomials
3. (x + 2) (x + 5)
4. (3x + 10) (2x – 5)
1. 2x2 * 5x3 = 10x5
monomial and a polynomial
polynomial by a polynomial
2. 2x2 (3x3 – 4x2 + x – 5)
5. (x + 2) (x2 + 5x + 6)
6x5 – 8x4 + 2x3 – 10x2
6. (x2 – 2x + 1) (x2 + 5x + 6)

7. Long Division
For Polynomials

8. Divide a Polynomial by a Binomial
Just like in elementary school…
Divide
Multiply
Subtract Add the Opposite
Bring Down
If there is a remainder… write it as a fraction.
Like with decimals, you may need a placeholder.
Ex:
(x2 – 10x – 24 ) ÷ (x + 2)
(8x4 – 4x2 + x +4) ÷ (2x + 1)
(x3 + y3) ÷ (x + y)

9. You Try 1. (3a4 – 6a3 – 2a2 + a – 6) ÷ (a + 1)
2. (t2 + 3t – 9) ÷ (5 – t ) Hint: reorder the denominator
3. (3x3 – 5x2 + 10x – 3) ÷ (3x + 1)

10. Polynomial Division Worksheet Classwork (1-10) Homework (11-20)

11. Exit Ticket
What are the 4 steps for Polynomial Long Division?