Chapter 5

1. Chapter 5 5.1 Polynomials and Functions

2. an n n n– 1 a0 an 0 leading coefficient an constant term degree a0 n descending order of exponents from left to right. A polynomial function is a function of the form f(x) = an xn+ an– 1xn– 1+· · ·+ a1x + a0 Where an 0 and the exponents are all whole numbers. For this polynomial function, an is the leading coefficient, a0 is the constant term, and nis the degree. A polynomial function is in standard form if its terms are written in descending order of exponents from left to right.

3. Degree Type Standard Form You are already familiar with some types of polynomial functions. Here is a summary of common types ofpolynomial functions. 0 Constant f (x) = a0 1 Linear f (x) = a1x + a0 2 Quadratic f (x) = a2x2+a1x + a0 3 Cubic f (x) = a3x3+ a2x2+a1x + a0 4 Quartic f (x) = a4x4 + a3x3+ a2x2+a1x + a0

4. Identifying Polynomial Functions 1 f(x) = x2– 3x4– 7 2 1 Its standard form is f(x) = –3x4+x2 – 7. 2 Decide whether the function is a polynomial function. If it is, write the function in standard form and state its degree, typeand leading coefficient. SOLUTION The function is a polynomial function. It has degree 4, so it is a quartic function. The leading coefficient is – 3.

5. Identifying Polynomial Functions f(x) = x3+ 3x Decide whether the function is a polynomial function. If it is, write the function in standard form and state its degree, typeand leading coefficient. SOLUTION The function is not a polynomial function because the term 3xdoes not have a variable base and an exponentthat is a whole number.

6. Identifying Polynomial Functions f(x) = 6x2+ 2x–1+ x Decide whether the function is a polynomial function. If it is, write the function in standard form and state its degree, typeand leading coefficient. SOLUTION The function is not a polynomial function because the term2x–1has an exponent that is not a whole number.

7. Identifying Polynomial Functions f(x) = –0.5x+x2– 2 Its standard form is f(x) = x2– 0.5x– 2. Decide whether the function is a polynomial function. If it is, write the function in standard form and state its degree, typeand leading coefficient. SOLUTION The function is a polynomial function. It has degree 2, so it is a quadratic function. The leading coefficient is .

8. Identifying Polynomial Functions 1 f(x) = x2– 3x4– 7 2 f(x) = –0.5x+ x2– 2 Polynomial function? f(x) = x3+ 3x f(x) = 6x2+ 2x–1+ x

9. Test 1, 2 Decide whether the function is a polynomial function. If it is, write the function in standard form and state the degree and leading coefficient.

10. Goal 1: To evaluate polynomial functions Goal 2: To simplify polynomial functions

13. Chapter 5 5.2 Addition and Subtraction of Polynomials Goal 1: To add polynomial functions Goal 2: To subtract polynomial functions

15. The additive inverse of a polynomial. The additive inverse of a polynomial can be found by replacing each term by its additive inverse. The sum of a polynomial and its additive inverse is O.

17. The additive inverse of a polynomial. The additive inverse of a polynomial can be found by replacing each term by its additive inverse. The sum of a polynomial and its additive inverse is O. Thus, to subtract one polynomial from another, we add its additive inverse.

20. Test 1, 2 Simplify the polynomial

21. HW #5.1-2Pg 208-209 1-29 Odd, 30-36Pg 212-213 1-31 Odd, 33-35

22. HW Quiz HW #5.1-2Saturday, May 31, 2014

23. Chapter 5 5.3 Multiplication of Polynomials

33. Test Find the product.

34. Challenge Simplify.

35. Based on your answers to parts to the above, write a general formula. Use “2n” to represent a general even integer and let “2n + 1” represent a general odd integer, and use “…” for missing terms.

36. Answers to challenge

37. HW #5.3Pg 217-218 1-39 Odd, 40-49

38. HW Quiz HW #5.3Saturday, May 31, 2014

39. Missing Parts 5.4 Factoring Do Examples from Regular book la205bad HW 5.4 Pg 222-223 3-60 Every Third, 61-76 5.5 More Factoring HW Handout Factoring 5.6 Factoring A General Strategy Do bonus problems from Great Factoring Problems WS HW Pg 231 1-37 Odd, 38-47

40. Row 1, 3, 5 Factor Completely 1. 2. 3. 4. Row 2, 4, 6 Factor Completely 1. 2. 3. 4. HW Quiz HW #5.6Saturday, May 31, 2014

41. 5.7 Solving by Factoring

44. HW #5.7Pg 233 1-42 Left Column, 43-46Pg 228 89-99 Odd

45. 5.8 Using Polynomial Equations

47. A candy factory needs a box that has a volume of 30 cubic inches. The width should be 2 inches less than the height and the length should be 5 inches greater than the height. What should the dimensions of the box be?

48. For the city park commission, you are designing a marble planter in which to plant flowers. You want the length of the planter to be six times the height and the width to be three times the height. The sides should be one foot thick. Since the planter will be on the sidewalk, it does not need a bottom. What should the outer dimensions of the planter be if it is to hold 4 cubic feet of dirt?

49. Suppose you have 250 cubic inches of clay with which to make a rectangular prism for a sculpture. If you want the height and width each to be 5 inches less than the length, what should the dimensions of the prism be?

50. HW #5.8a Pg 235-236 1-17 Odd, 18-20