Algebra - Polynomials

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Algebra

A branch of mathematics characterized by the use of variables and operations relating these variables.

Importance of Algebra

Algebra serves as a foundation of various concepts and applications of mathematics.

How can Algebra be used in real life?

An engineer uses algebra to solve physical problems such as how to build a bridge or design a house.

Businessmen use algebra to calculate costs, revenues, and profits.

Bankers use Algebra to calculate interests

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Word Problem

A Filipino citizen is said to be of legal age when he or she turns 18 years old. Romulo, who is a Filipino, was born in 2001.​

a. In what year will he be of legal age?

Solution: 2001 + 18 = 2019

b. In what year will he be 30 years old?

Solution: 2001 + 30 = 2031

c. In what year will he be 65 years old?

Solution: 2001 + 65 = 2066

Questions (Word Problem)

2001 + 18

2001 + 30

2001 + 65

a. What is the commonality among the solutions?​

2001 does not change.

b. What is the difference among the solutions?

The addend changes depending on the given age.

Constant & Variable

A constant represents a fixed value. Any number in an expression is a constant.​

A variable is a symbol used to represent values that can change or vary in an expression

Example:

2001 + n

Constant = 2001

Variable = n

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Everyday Constants and Variables

The electric bill each month - Variable

The number of days in a week​ - Constant

The number of hours of daylight in a day - Variable

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Algebraic Expressions

An algebraic expression is a combination of one or more constants, and variables along with at least one mathematical operation.

Examples: 70r, 70(r), 3x/2y

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Translating English Phrases to Mathematical Symbols

Addition:

The sum of a number and 2​

(or 2 + x since addition is commutative – can be reversed)​

2 added to a number​

2 more than a number​

A number increased by 2​

2 greater than x​

exceeds x by 2​

total of a number and 2​

can be translated to:

x + 2

Subtraction:

the difference of x and 2​

a number x decreased by 2​

x reduced by 2​

x take away 2​

a number x less 2​

2 subtracted from x​

2 less than x​

can be translated to:

x - 2

Multiplication:

2 times x​

the product of 2 and x​

2 multiplied by x​

twice x​

can be translated to:

2x

Division:

x divided by 2

the quotient of x and 2​

the ratio of x to 2​

can be translated to:

x ÷ 2

Exponents:

x raised to 2

can be translated to:

x^2

Note: "^" is the symbol for exponents.