ALGEBRAIC EXPRESSION LESSON 1

1. INTRODUCING THE LANGUAGE OF
ALGEBRA

2. Activity : Hunt Me!
Let’s Find Out: What are the basic terms in
algebra?
Let’s Use These Materials: Math notebook and
ballpen
Let’s Do It This Way: Inside the key is a list of
words which are commonly called “the language
of Algebra”. Find these words in the puzzle
below to open the treasure chest. Copy the
puzzle in your Math notebook and encircle

4. DEFINITION OF TERMS
• VARIABLES- symbols or letters that may have one
or more than one value
• CONSTANTS- are numbers that have fixed values
• ALGEBRAIC EXPRESSIONS - is an expression that
is made up of one or more terms
• TERMS- is a constant , a variable , or a product or
quotient of constants and variable
-separated by + or - sign

5. EXAMPLES
ALGEBRAIC EXPRESSIONS CONSTANT VARIABLE
3x+5 3,5 x
1
2

6. • EXPONENT - a number that indicates the number of
times a variable or a number is used as a factor
𝑥2
x is the base , 2 is the exponent
means 𝑥2
=(x)(x)

7. • Term is a constant, a variable or a product of
constant and variable.
• In the term 3x2, 3 is called the numerical coefficient
and
x2 is called the literal coefficient.
• In the term –x has a numerical coefficient which is -1
and a literal coefficient which is x.
• The term 5 is called the constant, which is usually
referred to as the term without a variable.

8. • Numerical coefficient is the constant/number.
• Literal coefficient is the variable including its
exponent.
• The word Coefficient alone is referred to as
the numerical coefficient.
• In the literal coefficient x2, x is called the base
and 2 is called the exponent.

9. • Degree is the highest exponent or the
highest sum of exponents of the
variables in a term.
• In 3x2 – x + 5, the degree is 2.
• In 3𝑥2
𝑦3
− 𝑥4
𝑦3
the degree is 7
• Similar Terms are terms having the same
literal coefficients.

10. POLYNOMIALS
• A polynomial is a kind of algebraic expression where each
term is a constant, a variable or a product of a constant and
variable in which the variable has a whole number (non-
negative number) exponent. A polynomial can be a monomial,
binomial, trinomial or a multinomial.
• An algebraic expression is NOT a polynomial if
1) the exponent of the variable is NOT a whole number {0, 1, 2,
3..}.
2) the variable is inside the radical sign.
3) the variable is in the denominator.

11. EXAMPLES:

12. EXAMPLES:
• WRITE EACH EXPRESSIONS IN
EXPANDED FORM:
1. ab= 2. 7𝑥2
3. -15xy
4. 12a 5. 8𝑦2

13. Continuation:
6. 28𝑥2
𝑦2
7. −32𝑥𝑦2
8. −50𝑎2
b
9. 19b
10. 45𝑐2
y

14. CLASSIFICATION OF ALGEBRAIC EXPRESSIONS
ACCDG TO NO. OF TERMS
• MONOMIALS - one term
• BINOMIALS- two terms
• TRINOMIALS -three terms
• POLYNOMIALS - FOUR OR MORE TERMS

15. EXAMPLES:

16. EXAMPLES:
CLASSIFY EACH ALGEBRAIC EXPRESSIONS
ACCORDING TO THE NUMBER OF TERMS
1. 3x 5. x(6xy)
2. 12x -3y-1
3. 5y-1
4. 7x-11y

17. Continuation:
6. (4𝑚)3
7. -2xy
8. 8(𝑎2
− 𝑏2
)
9. 3x - 2y + 5
10.
1
2
ab + 4

18. KINDS OF POLYNOMIAL ACCDG. TO DEGREE
1) Constant – a polynomial of degree zero
2) Linear – a polynomial of degree one
3) Quadratic – a polynomial of degree two
4) Cubic – a polynomial of degree three
5) Quartic – a polynomial of degree four
6) Quintic – a polynomial of degree five

19. * The next degrees have no universal
name yet so they are just called
“polynomial of degree ____.”
• A polynomial is in Standard Form if its
terms are arranged from the term with
the highest degree, up to the term with
the lowest degree.

20. • If the polynomial is in standard form the
first term is called the Leading Term, the
numerical coefficient of the leading
term is called the Leading Coefficient
and the exponent or the sum of the
exponents of the variable in the
leading term is the Degree of the
polynomial.

21. 2𝑥2
− 5𝑥5
− 2𝑥3
+ 3𝑥 − 10
The standard form of the above expression is
−5𝑥5
−2𝑥3
−2𝑥2
+ 3𝑥 − 10
LEADING TERM is −5𝑥5
LEADING COEFFICIENT is -5
DEGREE is 5
It is a quintic polynomial because its degree is
5.

22. ACTIVITY
COMPLETE THE TABLE.

23. Continuation:
• Identify the exponent, base and coefficients of the each
expression.
1. 7𝑎3
2. 3𝑥2
3. 10a
4. 25𝑚3
5. 40𝑥5