1. Warm up

2. Operations with polynomials
5.1

3. Product of Powers Property:
am an = am+n
Examples:
1. x7x w5w 3. n12n20

4. Power of a Power Property:
(am)n = amn
Examples:
1. (a5) (h6h3)2 3. ((q3)2)4

5. Power of a Product Property:
(ab)m = ambm
Examples:
1. (xy) (a2b) (2pq3)7

6. Negative Exponent Property:
Examples: 1. 2. 3.

7. Quotient of Powers Property:
Examples: 1. 2.

8. Zero Exponent Property:
a0 = 1
Examples:
1.x
3. 3x (3x) x

9. Power of a Quotient Property:
Examples: 1. 2. 3.

10. When are you done simplifying?

11. The trick is to put all 7 laws together.

12. The trick is to put all 7 laws together.

13. Polynomials All the coefficients are real numbers (not imaginary)
Exponents are whole numbers (positive integers)
NO variables in the denominator
NO radicals of variables
The degree of the polynomial is the degree of the monomial with the greatest degree.

14. Examples: Answer these questions for the following functions.

15. Examples: Simplify the polynomial.
1. (4x2 – 9x + 3) + (–2x2 – 5x – 6)
2. (2a3 + 5a – 7) – (a3 – 3a + 2)

16. Examples: Simplify the polynomial.
3. –y3(4y2 + 2y – 3)
4. (2x + 1) (4x2 + x – 5)

17. Examples: Simplify the polynomial.

18. Examples: Simplify the polynomial.