Algebraic Expressions and Polynomials

1. Algebraic
Expressions
and
Polynomials
2 0 2 3 - 2 0 2 4

2. Definitions
Constant
 any number is constant such
as 2, 4, 7, 35.
 any symbol that has a fixed
value is a constant such as
π, since it’s value is
approximately 3.1416.
Variable
 any letter or symbol that is
used to represent an
unknown number is a
variable such as a, n, m, k, x,
y,Ѳ.
Algebraic Expressions
-is a mathematical
phrase that uses
variables, numerals and
operation symbols.
Examples of Algebraic
Expressions:
3x + 2 7 + y
3𝑎
5
x – y 4a 5ab

3. Week 1
Parts of a Term
a.
7
13
𝑦 b. 11(𝑎 + 𝑥2
)
Numerical Coefficient of a
term is the constant factor
of the term (a.
7
13
, b. 11)
Literal Coefficient of a
term is the variable factor
of a term{a. 𝑦, b. (𝑎 + 𝑥2)}
Try it yourself!!!
Answer Key

4. Try it yourself!!!
Algebraic Expression
3𝑥 − 4 = 12
 3 is the numerical
coefficient
 𝑥 is the literal
coefficient or variable
 4 and 12 are
constants
 3𝑥 − 4 and 12 are
two separate
expressions
Answer Key

5. Simplifying Algebraic
Expressions
Simplification of an algebraic
expression can be defined as
the process of writing an
expression in the most
efficient and compact form
without affecting the value
of the original expression.
The process entails collecting
like terms, which implies
adding or subtracting terms
in an expression.
Steps in Simplifying
Algebraic Expressions
 Remove any grouping symbol
such as brackets and
parentheses by multiplying
factors
 Use the exponent rule to
remove grouping if the
terms are containing
exponents.
 Combine the like terms by
addition or subtraction
 Combine the constants

6. Examples:
Simplify the following:
a. 3𝑥2 + 5𝑥2
3𝑥2 + 5𝑥2 = 3 + 5 𝑥2
= 8 𝑥2
= 8𝑥2
Since both terms have the same
exponent, we combine them.
b. 2 + 2𝑥(6𝑥 + 4 + 2)
= 2 + (12𝑥2
+ 8𝑥 + 4𝑥)
= 12𝑥2
+ 12𝑥 + 2
Eliminate parenthesis by
multiplying any number outside it.
Add like terms.
Try it yourself!!!
Evaluate the following algebraic
expressions:
a. 3𝑥 + 2 𝑥 − 4
b. 2𝑦 + 5 − 7𝑦 + 8𝑥 − 8𝑥2
Answer Key
Evaluate the following algebraic
expressions:
a. 5𝑥 − 8
b. −8𝑥2 + 8𝑥 − 5𝑦 + 5

7. Translating Verbal
Expressions into
Algebraic Expressions
Algebra
sometimes defined as the
science of signs and symbols
solution of most mathematics
problem depends upon the
language of algebra by using
the various signs, symbols and
notations in algebra
Addition

8. Subtraction Multiplication

9. Examples:
a. Four times a number is five
less than the square of a
number.
Division
Power
Four times a number is five less than the
square of a number.
4 * x = 𝑥2
− 5
𝟒𝒙 = 𝒙𝟐 − 𝟓
b. True or False
Six times a number is Fifty-
four.
6𝑥 = 54
True

10. Week 1
Try it yourself!!!
Three more than
seven times a number
is nine more than five
times the number.
Answer:
Try it yourself!!!
When twelve is
subtracted from five
times some number,
the result is two less
than the original
number.
Answer:

11. Kinds of Polynomials
Polynomials
From Greek words
 poly meaning “many” and
nominal meaning “terms” or
“many terms”
 any expressions in the form
𝑎𝑛𝑥𝑛
+ 𝑎𝑛−1𝑥𝑛−1
+ ⋯ + 𝑎1𝑥 +
𝑎0 where n is a nonnegative
integer and the coefficients
𝑎0 ,….., 𝑎𝑛1 are real numbers
 no negative exponents
 no fractional exponents
 no variables in the
denominator
1. MONOMIAL – an expression
which contains only one term.
(ex. 5a, 4, 7x3)
2. BINOMIAL – an expression
which contains exactly two terms.
(ex. 𝑥2 + 3𝑥, 5x – y)
3. TRINOMIAL – an expression
which contains exactly three terms.
(ex. 𝑦3 + 2𝑦2 − 3𝑦,4𝑎2 − 𝑎 + 7)
4. MULTINOMIAL – an
expression which contains more
than three terms.

12. Degree of Polynomials
 Constant is a polynomial of degree
zero.
 Linear is a polynomial of degree
one.
 Quadratic is a polynomial of degree
two
 Cubic is a polynomial of degree
three.
 Quartic is a polynomial of degree
four
 Quintic is a polynomial of degree
five.
 The succeeding degree is termed
as 6th , 7th, 8th …. nth degree.
Degree of Polynomial
with Only One Term

13. Degree of Polynomials
with Two or More Terms
Try it yourself!!!
Evaluate the following polynomials by
completing the table below

14. Answer Key _END_
Prepared by:
Mr. Jb Sapaden
Instructor III, UBSHS