The document defines a polynomial function as a function where the variable has only non-negative integer exponents and is not in the denominator or inside a radical symbol. It gives the standard form of a polynomial function as P(x) = anxn + an-1xn-1 + ... + a1x + a0, where n is a non-negative integer, the ai values are coefficients, anxn is the leading term, an is the leading coefficient, and a0 is the constant term. It also discusses rewriting polynomial functions between standard and factored forms.

1. POLYNOMIAL FUNCTION
P(𝑥) = 𝑎𝑛𝑥𝑛
+ 𝑎𝑛−1𝑥𝑛−1
+ 𝑎𝑛−2𝑥𝑛−2
+ … + 𝑎1𝑥 + 𝑎0
Where n is a nonnegative integer, 𝑎0, 𝑎1, … 𝑎𝑛 are
real numbers called coefficients, 𝑎𝑛𝑥𝑛
is the leading
term, 𝑎𝑛 is the leading coefficient, and 𝑎0 is the
constant term

2. POLYNOMIAL FUNCTION
P(𝑥) = 𝑎𝑛𝑥𝑛 + 𝑎𝑛−1𝑥𝑛−1 + 𝑎𝑛−2𝑥𝑛−2 + … + 𝑎1𝑥 + 𝑎0
Where n is a nonnegative integer, 𝑎0, 𝑎1, … 𝑎𝑛 are
real numbers called coefficients, 𝑎𝑛𝑥𝑛
is the leading
term, 𝑎𝑛 is the leading coefficient, and 𝑎0 is the
constant term

3. POLYNOMIAL FUNCTION
P(𝑥) = 𝑎𝑛𝑥𝑛 + 𝑎𝑛−1𝑥𝑛−1 + 𝑎𝑛−2𝑥𝑛−2 + … + 𝑎1𝑥 + 𝑎0
Example:
P(x) = 3x2
+ 5x - 7

4. A function is a POLYNOMIAL FUNCTION if:
• The VARIABLE has no negative exponent.
• The VARIABLE has no fractional exponent.
• The VARIABLE is not inside the radical symbol.
• The VARIABLE is not in the denominator.

5. A function is a POLYNOMIAL FUNCTION if:
• The VARIABLE has no negative exponent.
• The VARIABLE has no fractional exponent.
• The VARIABLE is not inside the radical symbol.
• The VARIABLE is not in the denominator.
P(x) = 2x3
- 4x + 5
√

6. A function is a POLYNOMIAL FUNCTION if:
• The VARIABLE has no negative exponent.
• The VARIABLE has no fractional exponent.
• The VARIABLE is not inside the radical symbol.
• The VARIABLE is not in the denominator.
P(x) = x−4
+ 6x + 5
X

7. A function is a POLYNOMIAL FUNCTION if:
• The VARIABLE has no negative exponent.
• The VARIABLE has no fractional exponent.
• The VARIABLE is not inside the radical symbol.
• The VARIABLE is not in the denominator.
P(x) = x
3
2 - 7x3
+ 2
X

8. A function is a POLYNOMIAL FUNCTION if:
• The VARIABLE has no negative exponent.
• The VARIABLE has no fractional exponent.
• The VARIABLE is not inside the radical symbol.
• The VARIABLE is not in the denominator.
P(x) = x + 3x - 2
X

9. A function is a POLYNOMIAL FUNCTION if:
• The VARIABLE has no negative exponent.
• The VARIABLE has no fractional exponent.
• The VARIABLE is not inside the radical symbol.
• The VARIABLE is not in the denominator.
P(x) =
5
x3 - 7x2
+ 2x + 4
X

10. Degree:
Leading Term:
Leading Coefficient:
Constant Term:
P(x) = 2x3
- 4x + 5
2x3
2
5
3

11. Degree:
Leading Term:
Leading Coefficient:
Constant Term:
f(x) = 2x + x3
+ 1

12. Rewriting Polynomial Function in Standard Form
f(x) = 2x + x3
+ 1 f(x) = x3
+ 2x + 1

13. Degree:
Leading Term:
Leading Coefficient:
Constant Term:
f(x) = 2x + x3
+ 1
x3
1
1
f(x) = x3
+ 2x + 1
3

14. Degree:
Leading Term:
Leading Coefficient:
Constant Term:
y = x3
(x2
+ 4)

15. Writing Polynomial Function From Factored Form to
Standard Form
y = x3
(x2
+ 4) y = x5
+ 4x3

16. Degree:
Leading Term:
Leading Coefficient:
Constant Term:
y = x3
(x2
+ 4)
x5
1
0
y = x5
+ 4x3
5