The document discusses characteristics and parts of a polynomial expression. A polynomial expression is an algebraic expression with multiple terms that can contain variables and exponents. Key parts of a polynomial expression include: the expression itself, terms, coefficients, variables, exponents, and constants. An example polynomial expression is worked through to illustrate these different parts.

1. HOW ARE YOU
to find out?
Select an emoji that will describe your day.

2. LET’S TRY THIS FIRST!
2
Circle the variable(s) in each expression:
3𝑥2 – 2𝑥 + 5
7𝑎
𝑥2 + 3 + 2𝑦

3. CHARACTERISTICS
AND PARTS OF A
POLYNOMIAL
EXPRESSION
PREPARED BY: MR. JERRY MAE A. RANES

4. POLYNOMIAL
4
▪ “poly” means many
▪ “nomial” means terms

5. 5
CHARACTERISTICS OF A
POLYNOMIAL EXPRESSION

6. CHARACTERISTICS OF A
POLYNOMIAL EXPRESSION
▪ Polynomial can have:
▪ constant, variables,
and exponent
▪ only nonnegative
exponent
▪ only finite number of
terms
6
▪ Polynomial cannot have:
▪ variables in the
denominator
▪ fractional exponents
▪ negative exponents
▪ roots of variables
▪ infinite number of terms

7. 7
PARTS OF A POLYNOMIAL
EXPRESSION

8. 8
EXPRESSION
TERM
COEFFICIENT
VARIABLE
EXPONENT
CONSTANT
OPERATORS
PARTS OF A POLYNOMIAL
EXPRESSION

9. 9
Expression
a group of numbers, symbols, and operators, that indicates a
value.
Terms
each individual portion of the expression. It can be a number,
variable, or the product of a number & a variable
Numerical
Coefficient
a number that multiplies a variable or variables in a term.
Literal Coefficient a variable or variables that multiply each other in a term.
Variable a symbol for an unknown value
Exponent
a value indicating the number of times the base should be
multiplied by itself
Constant any number by itself, the number does not change
Operators
are symbols such as +, −,×,÷, that indicate the necessary
process to handle terms

10. 10
𝟒𝒙𝟐
+ 𝒙 − 𝟗
ILLUSTRATIVE EXAMPLE #1
Expression 4𝑥2
+ 𝑥 − 9 Variable 𝑥
Term 4𝑥2
, 𝑥, and −9 Exponent 2 and 1
Numerical
Coefficient
4 and 1 Constant −9
Literal
Coefficient
𝑥2
and 𝑥 Operators +, −, and ×

11. ILLUSTRATIVE
EXAMPLE
11

12. 12
SEATWORK #1
Identify the coefficient, constant, exponent, and variable of the
following polynomial expression:
POLYNOMIAL
EXPRESSION
COEFFICIENT VARIABLE EXPONENT CONSTANT NO. OF TERMS
3𝑥2
+ 4𝑥 − 7
2𝑦3
− 5𝑦2
+ 6𝑦
4𝑧
7
2𝑎5
− 4𝑏