Definitions [9]
A variable is a symbol, usually a letter (like x, y, or z), representing an unknown or changeable numerical value in an equation or an algebraic expression.
A constant is a fixed value that does not change.
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Examples: 5, −7, 256
Terms having the same literal part (same variables with the same powers) are called like terms.
For example:
xy, 5xy, -4xy, etc. are like terms
The terms that do not have the same literal coefficients are called unlike terms.
For example:
6a, 6ab and 6ac are unlike terms.
A factor of a number is any number that divides the given number completely without leaving a remainder.
or
When two numbers are multiplied, the result is called their product, and the numbers that are multiplied are called factors of the product.
A common factor of two or more numbers is a number that divides each of the given numbers exactly, without leaving any remainder.
When an algebraic expression is made of only one variable, it is called a polynomial in one variable.
Examples of Polynomials in One Variable:
| Polynomial | Variable | Why it’s a polynomial |
|---|---|---|
| 3 + 5x − 7x2 | x | All exponents (0, 1, 2) are whole numbers |
| 9y3 − 5y2 + 8 | y | All exponents (3, 2, 0) are whole numbers |
| z4 + z - 1 | z | All exponents (4, 1, 0) are whole numbers |
A polynomial is an algebraic expression made up of terms in which the variables have non‑negative whole-number exponents.
The degree of a polynomial is simply the highest exponent (power) in the expression.
Example 1: 4x² - 3x⁵ + 8x⁶
- Term 1: 4x² → exponent = 2
- Term 2: -3x⁵ → exponent = 5
- Term 3: 8x⁶ → exponent = 6
- Degree = 6 (highest exponent)
Example 2: 25 - x⁴
- Term 1: 25 → exponent = 0 (since 25 = 25x⁰)
- Term 2: -x⁴ → exponent = 4
- Degree = 4
