The document outlines the characteristics of polynomial expressions and functions, distinguishing between polynomial expressions (PE) and non-polynomial expressions (NPE). It explains that polynomial functions must have non-negative integer exponents and be in standard form, which organizes terms in descending order of their degree. Additionally, it describes the components of a polynomial function, such as leading term, leading coefficient, and constant term.

1. POLYNOMIAL
FUNCTION
Prepare by: JUDY ANN Q. DACAWAN

2. Which is which?
Determine whether each
of the following is a
Polynomial Expression
(PE) or Not Polynomial
Function (NPE).

3. 14x3
PE or NPE

4. 5x3
-4 + x
PE or NPE

5. -20xy3
xy43
PE or NPE

6. -
PE or NPE

7. x
PE or NPE

8. PE or NPE
+ xyz

9. ab-3
+ 2abc
PE or NPE

10. 𝐝𝟑
𝐝𝐞
𝟐
PE or NPE

11. 2x – 5xy
PE or NPE

12. 𝟑 𝐱
𝐱𝐲
PE or NPE

13. -
PE or NPE

14. 20x-3
+ 3y6
PE or NPE

15. - 20x24
- 3y61
PE or NPE

16. Not a Polynomial if the
variable has…
Negative exponent
Fractional exponent
Inside the radical sign
In the denominator

17. Polynomial Function
Algebraic expression
consist of one or more
summed terms…
Also called multinomial

18. P(x) = anxn
+ an-1xn-1
+ an-2x n-2
+ … + a1x1
+ a0
Where an ≠ 0

19. Standard form
Decreasing powers
of variable, the
polynomial function is
in standard form.

20. Standard form

21. Write the given polynomial
functions in Standard Form

22. Write the given polynomial
functions in Standard Form
P(x) = 3x2
+ 3x + 5x + 5
P(x) = 3x2
+ 8x + 5

23. P(x) = anxn
+ an-1xn-1
+ an-2x n-2
+ … + a1x1
+ a0
Where an ≠ 0

24. anxn -
leading term
anxn
-leading coefficient
a0 -constant term
anxn
- degree of
polynomial function

25. Leading term
Degree of P(x)
Constant term
Leading coefficient