1. 5.1 Operations with Polynomials

2. Recall these properties of exponents

3. (2k) 4 = (ab) 3 =

5. A. Simplify the expression Assume that no variable equals 0.

6. B. Simplify the expression. Assume that no variable equals 0.

7. C. Simplify the expression. Assume that no variable equals 0.

8. A.Simplify the expression. Assume that no variable equals 0.

9. Definitions Rules of Polynomial Functions There are no square roots of variables, no fractional powers, and no variables in the denominator of any fractions A monomial is an expression with one term.

11. Important Vocabulary The degree of a monomial is the sum of the powers of the variable The degree of a polynomial is the degree of the monomial with the highest degree.

13. C. Determine whether is a polynomial. If it is a polynomial, state the degree of the polynomial.

14. To simplify Polynomials, add like terms A. Simplify (4x 2 – 9x + 3) + (–2x 2 – 5x – 6).

15. B. Simplify (2a 3 + 5a – 7) – (a 3 – 3a + 2).

16. A. Simplify (3x 2 + 2x – 3) – (4x 2 + x – 5).

17. Use distributive Property Find –y(4y 2 + 2y – 3).

18. Find –x(3x 3 – 2x + 5).

19. Find (a 2 + 3a – 4)(a + 2).

20. Find (x 2 + 3x – 2)(x + 4).

21. Write a polynomial equation E-SALES A small online retailer estimates that the cost, in dollars, associated with selling x units of a particular product is given by the expression 0.001x 2 + 5x + 500. The revenue from selling x units is given by 10x. Write a polynomial to represent the profits generated by the product.