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# Polynomial function

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### Polynomial function

1. 1. Definition of Polynomial Function Reynaldo B. Pantino
2. 2. Objectives: 1. Define polynomial function. 2. Determine the degree and the number of term of polynomial function. 3. Identify polynomial function.
3. 3. Check out this! Identify whether the following are polynomial function or not. 1.) f(x) = 2x + 2 2.) f(x) = 5 3.) f(x) = x2 – x6 + x4 + 3 4.) f(x) = 3x3 – x2 + x – 3 5.) f(x) = x(x + y) 6.) f(x) = 4x3 – 3x2
4. 4. How do find the activity? What is your understanding in identifying whether the given function is polynomial? Is linear function and quadratic function a polynomial function?
5. 5. A polynomial function of degree n is a function of the form, f(x) = anxn + an-1xn-1 +an-2xn-2 + … + a0 where n is a nonnegative integer, and an , an – 1, an -2, … a0 are real numbers and an ≠ 0.
6. 6. Illustrative Examples. 1. The polynomial function f(x) = 5x3 + 2x2 + 6 has 3 terms The highest power of its term is 3 Therefore, the degree of the polynomial function is 3 2. The polynomial function g(x) = 4x2 + 2x3 – x4 + 3 has 4 terms The degree of the terms are 2, 3, 4 and 0 respectively. Therefore, the degree of g(x)is 4
7. 7. 3. The polynomial function h(x) = 6x4 + 2x3 + x2 – x + 4 has 5 terms The degree of terms are 4, 3, 2, 1 and 0 respectively. Therefore, the degree of h(x) is 4
8. 8. Exercises. Give the degree of each of the following polynomial functions. 1.) f(x) = 3x3 – x2 + x – 3 2.) f(x) = x2 – x6 + x4 + 3 3.) f(x) = 5x2 – 4x4 – 2 4.) f(x) = x + 2x2 + 3x3 + 6 5.) f(x) = 3x6 + 6x4 + x2 – x 6.) f(x) = 3x3 + 2x – x4 7.) f(x) = 5x + 4 8.) f(x) = x2 + x 9.) f(x) = 6x2 + x – 3 10.) f(x) = x2 – 2x + 3 11.) f(x) = 2x4 + x3 – 2x2 + 2 12.) f(x) = x5 – x4 + 1/4x + 3
9. 9. Questions to answer. 1. In order to identify the degree of a function, what is your consideration you make? 2. What is highest power? 3. How to determine the number of term of a function? 4. Give at least 2 examples of polynomial function of degree What’s 4 with 5 Your terms. Message? 5. Define polynomial function. 6. Is linear function and quadratic function a polynomial function?
10. 10. ASSIGNMENT. 1. What is remainder theorem? 2. Show the proof of remainder theorem. 3. Copy examples A and B in your notebook on page 95. Reference: Advanced Algebra, Trigonometry & Statistics. Pages 94 – 95.