2. • Al- Khwarizmi is the Father of Algebra.
• Abu Ja’far Muhammad ibn Musa al-Khwarizmi lived in
Baghdad around 780 to 850 CE (or AD).
• The word algebra comes from his book “Kitab Muhtasar
fi Hisab Al Gabr Wa I Muqabala” later translataed to
English (The Compendious Book of Calculation by
Completion and Balancing)
• Algebra was described as the science of ‘REDUCTION’
and ‘BALANCING’
Algebra
3. 1. Variables
Terms Related to
Algebra
• These are symbols or letters that may take one or
more than one value.
• These variables may represent elements of the set
of real numbers.
4. 2. Constants
Terms Related to
Algebra
• These are numbers or symbol which
has a fixed numerical value.
• For example: 2, 5, 0, -3, -7, etc. are
constants.
5. 3. Terms
Terms Related to
Algebra
• Term is a constant (number), a variable (letter) or
combination of both by a product or by a
quotient of constants and variables.
• Terms are separated by the symbols plus or
minus sign.
6. 3. Terms
Terms Related to
Algebra
• Term is a constant (number), a variable (letter) or
combination of both by a product or by a
quotient of constants and variables.
• Terms are separated by the symbols plus or
minus sign.
7. Terms Related to
Algebra
• Numerical coefficient – the constant factor in a given
algebraic expression. The number appears before a variable in a
term.
o In the expression -5x, the numerical coefficient is -5.
o In the expression 10𝑎3
𝑏, the numerical coefficient is 10.
• Literal coefficient – the variable including the exponent in a
term.
o In the expression 9𝑥2
, the literal coefficient is 𝑥2
.
3. Terms
8. Terms Related to
Algebra
Similar Terms – terms having the same literal coefficients.
o 𝟗𝒙𝟐 and 𝟑𝒙𝟐 are similar because their literal coefficients are the same.
o 𝟓𝒂𝟐 and 𝒂𝟑 are not similar because their literal coefficients are not the same.
o 𝟐𝒙𝒚𝟐 and −𝟑𝒙𝟐𝐲 are not similar because their literal coefficients are not the same.
3. Terms
9. Terms Related to
Algebra
4. Algebraic Expressions
These are mathematical phrases that may made
up of variables, constants, or combination of
both which may be related by any of the four
fundamental operations.
Note: it is only a phrase, not a sentence, therefore it does not include
relationship sign such as =, <, >, ≤, ≥ and others.
10. Terms Related to
Algebra
5. Degree
the highest exponent or the highest sum
of exponents of the variables in a term.
11. Terms Related to
Algebra
6. Leading Term
The term with the highest degree.
7. Leading Coefficient
The numerical coefficient of the leading
term.
14. What is a Polynomial?
Polynomials
Polynomial is a special type of algebraic
expression in which each term is a constant, or a
variable, or a constant multiplied by a positive
integral power of one or more variables.
17. When does an algebraic expression be a
polynomial?
Polynomials
Must not have rational/fractional exponent.
Must not have negative exponent.
Must not have variable/s in the denominator.
Must not have variable/s under the radical sign.
19. Polynomials according to number of terms:
Polynomials
Monomial – a polynomial with only one term.
Binomial – a polynomial with exactly two terms.
Trinomial – a polynomial with exactly three terms.
Multinomial – a polynomial with four or more terms.
20. Polynomials according to degree:
Polynomials
Constant – a polynomial with degree 0.
Linear – a polynomial with degree 1.
Quadratic – a polynomial with degree 2.
Cubic – a polynomial with degree 3.
Quartic – a polynomial with degree 4
Quintic – a polynomial with degree 5
𝒏𝒕𝒉
degree polynomial – use to describe polynomials with
degree 6 and more. (𝑛 is the degree of the polynomial)
22. The four mathematical operation:
Polynomials
Addition
Subtraction
Multiplication
Division
23. Addition and Subtraction of Polynomials
Polynomials
• Addition and Subtraction of Polynomials is
very simple:
1. Combine the similar terms.
2. Under similar terms just add/subtract its
numerical coefficients.
3. In case there are terms dissimilar to the other
just add it to the result (copy).
24. A review on addition and subtraction of
integers:
Polynomials
• Addition of Integers remember the:
SADS
“Same Add, Different Subtract”
25. Polynomials
• Addition of Integers
“Same Add, Different Subtract”
• Same sign add then follow the sign of the number.
• Different sign, Subtract then follow the sign of the
greater number.
27. Polynomials
• Subtraction of Integers
“Copy – Change – Change back to SADS”
• Copy the first number
• Change the operation to addition
• Change the sign of the second number
• Back to the addition rule.
30. Multiplication and Division of Polynomials
Polynomials
• Addition and Subtraction of Polynomials is
very simple:
1. Distributive Property.
2. Divide the numerical coefficients
3. Apply laws of exponents on the literal
coefficients.
31. A review on multiplying and dividing integers:
Polynomials
• In multiplying and Dividing remember the:
LPUN
“Like Positive, Unlike Negative”
32. Polynomials
• multiplying and Dividing Integers
“Like Positive, Unlike Negative”
• Sign of the Product and/or Quotient of like sign
(same sign) always positive.
• Sign of the Product and/or Quotient of unlike sign
(different sign) always negative.
33. A review on Laws of Exponents:
Polynomials
• In multiplying and Dividing remember the:
LPUN
“Like Positive, Unlike Negative”
