1. Polynomial function Desirae O. Cecilia M.

2. Polynomial function A polynomial function is an expression of finite length A polynomial function is an expression of finite length For example, x2-x/4+7 is a polynomial For example, x2-x/4+7 is a polynomial

3. Polynomial functions A polynomial is either zero, or can be written as the sum of one or more non-zero terms A polynomial is either zero, or can be written as the sum of one or more non-zero terms Forming a sum of several terms produces a polynomial. For example, the following is a polynomial Forming a sum of several terms produces a polynomial. For example, the following is a polynomial

4. Real world The concentration, in parts per million, of a certain drug in the bloodstream after t hours is given by the polynomial -0.05t^2 + 2t + 2 Find the concentration after 2 hr. To find the concentration after 2 hr, we evaluate the polynomial for t = 2: -0.05t^2 + 2t + 2 = -0.05(2)^2 + 2(2) + 2 --------------------------= -0.05(4) + 4 + 2 ---------------------------= -0.2 + 4 + 2 ---------------------------= 5.8 The concentration after 2 hr is 5.8 parts per million. The concentration, in parts per million, of a certain drug in the bloodstream after t hours is given by the polynomial -0.05t^2 + 2t + 2 Find the concentration after 2 hr. To find the concentration after 2 hr, we evaluate the polynomial for t = 2: -0.05t^2 + 2t + 2 = -0.05(2)^2 + 2(2) + 2 --------------------------= -0.05(4) + 4 + 2 ---------------------------= -0.2 + 4 + 2 ---------------------------= 5.8 The concentration after 2 hr is 5.8 parts per million.

5. Polynomial function Zero of Multiplicity k If is a factor of a polynomial function f and Zero of Multiplicity k If is a factor of a polynomial function f and is not a factor of f, then r is called a zero of multiplicity k of f. is not a factor of f, then r is called a zero of multiplicity k of f.

6. Nature Where are polynomial functions found in nature? Where are polynomial functions found in nature? If you look at a cross section of a honeycomb, you see a pattern of hexagons. This pattern is one hexagon, surrounded by 6 more hexagons, surrounded by 12 hexagons, etc. The total number of hexagons can be modeled by f(x) = 3r2 – 3r + 1, where r is the number of rings and f(r) is the number of hexagons. If you look at a cross section of a honeycomb, you see a pattern of hexagons. This pattern is one hexagon, surrounded by 6 more hexagons, surrounded by 12 hexagons, etc. The total number of hexagons can be modeled by f(x) = 3r2 – 3r + 1, where r is the number of rings and f(r) is the number of hexagons.

7. Graphs

8. Examples EX: 3x5 + 2x4 – 5x3 + x2 + 1 EX: 3x5 + 2x4 – 5x3 + x2 + 1 n = 5, a0 = 3, a1 = 2, a2 = -5, a3 = 1, a4 = 0 and a5 = 1 n = 5, a0 = 3, a1 = 2, a2 = -5, a3 = 1, a4 = 0 and a5 = 1

9. Example 5x3 − 4x2 + 7x − 8. 5x3 − 4x2 + 7x − 8.

10. Example EX: 3x5 + 2x4 – 5x3 + x2 + 1 EX: 3x5 + 2x4 – 5x3 + x2 + 1 n = 5, a0 = 3, a1 = 2, a2 = -5, a3 = 1, a4 = 0 and a5 = 1

11. Example

12. Nature

13. Real World

14. Nature