1. Exponents, Radicals, Polynomials…
Unit 2
Exponents, Radicals, Polynomials…

2. Exponent Rules & Monomials
Multiplying powers
Dividing powers
Power to a power
Negative exponents
Zero as an exponent
Use 5-1 sheet

3. Polynomials Non-Examples: 10/x, 5x-5 – 3x Rules for polynomials
Monomials (variables attached to numbers—no negative or fraction exponents) connected by addition or subtraction
Examples:
5xy , 10x³y + ½ yz – 2xyz
Non-Examples:
10/x, 5x-5 – 3x

4. Adding Polynomials-Combine Like Terms
Add the following polynomials: (3a2 + 3ab - b2) + (4ab + 6b2)
(4x2 - 2xy + 3y2) + (-3x2 - xy + 2y2)
(9y - 7x + 15a) - (-3y + 8x - 8a)
(7a - 10b) - (3a + 4b)

5. Multiplying Polynomials
3x(3x² + 5xy³) Distribute!!!
(7x – 3)(-2y + 5x) FOIL!!!
(2x – 4)(x² + 3x – 5) Double distribute!!!
Use sheet 5-2

6. Dividing Polynomials Polynomial by a monomial 5a²b – 15ab³ + 10a³b4

7. On your own…
6k²m – 12k³m² + 9m³
2km²

8. Long Division of polynomials
(x² - 2x – 15) divided by (x – 5)

9. (a² - 5a + 3)(2 – a)-1
Hint: put the variable in the front…

10. (4y4 – 5y² + 2y + 4) / (2y – 1)

11. Synthetic Division When do we use synthetic division?
(x³ - 4x² + 6x – 4) / (x – 2)
Set binomial = 0 and solve for x. 2|
|0 ---remainder
So…the bottom row are the coefficients
x² - 2x + 2

12. How do we know… When to just “cancel” terms?
When to use long division?
When to use synthetic division?