topic in math 4

1. Definition of Polynomial
Function
Reynaldo B. Pantino

2. Objectives:
1. Define polynomial function.
2. Determine the degree and the
number of term of polynomial function.
3. Identify polynomial function.

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. 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. 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. 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. 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. 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. 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. 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.