This document defines key concepts in algebra including constants, variables, algebraic expressions, polynomials, and the degree of polynomials. It explains that constants represent fixed values while variables represent unknown numbers. Algebraic expressions use variables, numbers, and operations. Polynomials are expressions with no negative exponents or fractions containing terms with variables and their powers. The degree of a polynomial refers to the highest power of its terms, with monomials having one term, binomials two terms, and trinomials three terms. The document provides examples and exercises to illustrate these algebraic concepts.
2137ad Merindol Colony Interiors where refugee try to build a seemengly norm...luforfor
This are the interiors of the Merindol Colony in 2137ad after the Climate Change Collapse and the Apocalipse Wars. Merindol is a small Colony in the Italian Alps where there are around 4000 humans. The Colony values mainly around meritocracy and selection by effort.
More Related Content
Similar to Week 2 (Algebraivc Expressions and Polynomials).pptx
2137ad Merindol Colony Interiors where refugee try to build a seemengly norm...luforfor
This are the interiors of the Merindol Colony in 2137ad after the Climate Change Collapse and the Apocalipse Wars. Merindol is a small Colony in the Italian Alps where there are around 4000 humans. The Colony values mainly around meritocracy and selection by effort.
Hadj Ounis's most notable work is his sculpture titled "Metamorphosis." This piece showcases Ounis's mastery of form and texture, as he seamlessly combines metal and wood to create a dynamic and visually striking composition. The juxtaposition of the two materials creates a sense of tension and harmony, inviting viewers to contemplate the relationship between nature and industry.
Explore the multifaceted world of Muntadher Saleh, an Iraqi polymath renowned for his expertise in visual art, writing, design, and pharmacy. This SlideShare delves into his innovative contributions across various disciplines, showcasing his unique ability to blend traditional themes with modern aesthetics. Learn about his impactful artworks, thought-provoking literary pieces, and his vision as a Neo-Pop artist dedicated to raising awareness about Iraq's cultural heritage. Discover why Muntadher Saleh is celebrated as "The Last Polymath" and how his multidisciplinary talents continue to inspire and influence.
2137ad - Characters that live in Merindol and are at the center of main storiesluforfor
Kurgan is a russian expatriate that is secretly in love with Sonia Contado. Henry is a british soldier that took refuge in Merindol Colony in 2137ad. He is the lover of Sonia Contado.
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
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
Note: Numerical Expressions (e.g. 4+2, 35-7) is different from algebraic expressions(see slide for examples).
Ѳ(Theta) is a Greek letter symbol used to represent an angle, time constants or reluctance.
Give more examples of terms including symbolic constants such as pi, gravitational constants etc.
Give more examples of Algebraic Expressions and help them identify the numerical coefficients, literal coefficients, constants and expressions.
Note: All previous slides must be accomplished within 30 minutes.
Discuss examples of simplifying algebraic expressions while the definitions and steps are presented on screen as their guide.
Finish discussion within 40 minutes or less.
Discuss examples of simplifying algebraic expressions while the definitions and steps are presented on screen as their guide.