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• Find an expression representing the surface area and volume of a box with one edge unknown, a second edge one unit longer that the first edge, and the third edge one unit shorter than the first edge.
Chapter 9: Polynomial Functions
Lesson 1: Polynomial Models
Mrs. Parziale
Vocabulary
polynomial: a polynomial in (x) is an expression of the form
where (n) is a nonnegative integer and
Ex.
1 21 2 1 0....n n n
n n na x a x a x a x a
0na
4 3 23 7 5 10x x x x
Degree of a Polynomial
• For a polynomial in a single variable - the value of the highest exponent.
• For a polynomial of multiple variables - the largest sum of the exponents of the variables in any term of the polynomial.
More Vocab
• coefficient: numbers in front of the variables. (an, an-1, an-2, ...)
• leading coefficient: an (number in front of the variable with the largest exponent)
• standard form (for a polynomial function in 1 variable): the polynomial is written in descending order of exponents
1 21 2 1 0....n n n
n n na x a x a x a x a
Naming Polynomials
• Based on number of terms: –monomial - polynomial with one term –binomial – polynomial with two terms – trinomial – polynomial with three terms
Example 1:
• Given the polynomial
5x7 + 6x5 – 4x4 + 7x3 + 3x2 – 2 Identify:
(a) degree of the polynomial = ______
(b) leading coefficient = ___________
(c) all coefficients: ________________
(d) constant term = _____________
Example 2: • Suppose that each year since your 13th birthday, your parents have given you
money to save for college. The first year they give you $500, the next year 700, etc. (Each year they give you $200 more than the last year.) You invest it in an account paying 5% interest compounded annually. How much money will you have when you turn 17?
Birthday Expression Total
13 $
14 $
15 $
16 $
17 $
Example 2:
• Write a polynomial expression that represents the amount of money you will have at age 17. (In this case, x is the scale factor)
Birthday Expression Total
13 500 $500
14 500(1.05) + 700 $1225
15 500(1.05)2 + 700(1.05) + 900 $ 2186.25
16 500(1.05)3 + 700(1.05)2 + 900(1.05) + 1100 $ 3395.56
17 500(1.05)4 +700(1.05)3 +900(1.05)2 +1100(1.05) +1300
$ 4865.34
Example 3:
• Suppose a cube has a side of length (x+y).
a. Label the cube to the right.b. Write the volume of the cube
in expanded form. c. What is the degree of the
polynomial in Example 3?
Closure: Example 4
A company wants to construct a box. They take a 50” by 75” piece of cardboard, cut out a square of length (p) from each corner, and fold the box (with no lid).
a. Label the figure at the right.b. Express the volume of the box as a
polynomial in standard form.
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