1. POLYNOMIAL
FUNCTION

2. A polynomial function of a degree n is a
function of the form
 F(x)= An , An-1 Xn-1,A n-2X n-2 + . . . + A0
 When n is a nonnegative integer and
 An , An-1 Xn-1,A n-2X n-2 + . . . + A0 are real
numbers , and ≠ 0.

3. PARTS

4. Number of terms
 determined by the highest power
of its term
Example:
F(x)=2x 5 + x 2 –x + 2
Therefore, the degree (n) of f(x) is
5

5. Leading Coefficient
 Example:
 F(x) =8x 5 + 3x 4 + x – 10
Therefore, the leading coefficient (An)
of f(x) is 8

6. Leading Term
 Example:
F(x) =8x 5 + 3x 4 + x – 10
Therefore, the leading
coefficient (An) of f(x) is 8

7. Constant Term
 Example:
F(x)= x 5 – x 4 + 4x +3
Therefore, constant term
(A0) of f(x) is 3

8. By the Number of
Terms

9. Monomials
 consists of only one term
Example:
2x 3 ,5 , 6x 4 y, -4xy,…

10. Binomial
 consists of two terms
Example:
2a+b,x 2 + y 2 ,2x 3 + 6xy,
. ..

11. Trinomials
consists of three terms
Example:
X 2-2x +7, 5a b – 20, . . .
2 2

12. Multinomial
consists of four or more terms
Example:
8x 5 + 5x 2 + y +2y, 7x 3
y–y 3 +2x 4 y -3x,. . .

13. KINDS

14. By the Highest Power /
Degree

15. Linear
polynomial with a highest
power of one
Example:
7x+y, 3x ,5x+6

16. Quadratic
polynomial with a highest
power of two
Example:
X 2 + 7x + 10, X 2 + 9, X 2
+ y, . .

17. Cubic
polynomial with a highest
power of three
Example:
x 3 + 8, x 3 + 4x 2 +5x + 8,
...

18. Quartic
polynomial with a highest
power of four
Example:
7x 4 +2x 3 + 6x 2 +10, 8x 4
+9, . . .

19. Pentic
polynomial with a highest
power of five
Example:
10x 5 + 5,6x 5 +2x 3
+7,. . .