Characteristics and Parts of a Polynomial.pdf

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