More Algebra

EnchantedLearning.com Algebra Glossary Terms Used in Algebra

absolute value - The absolute value of a number is the distance from the origin on a number line. For example, the absolute value of 2 is 2 (written |2|=2). The absolute value of -2 is also 2 (written |-2|=2).

algebra - Algebra is the study of generalized arithmetic. In algebra, unknown numbers can be represented by letters in order to solve equations. For example, 4 + x = 10 is true for x=6. Algebra (originally called al-jabr, meaning "restoration") was invented in the Middle East by Abu Ja'far Muhammad ibn Musa Al-Khwarizmi (born in Baghdad about AD 825) during the Middle Ages.

coefficient - In an expression or equation, a coefficient is a number in front of a variable. For example, in the expression 8x, the coefficient is 8 (and the variable is x).

degree of a polynomial - The degree of a term within a polynomial is the sum of the exponents of variables that occur in that term (if there is no exponent written on a variable, such as in 3x, the exponent is one). The degree of a polynomial is the greatest degree of any term in the polynomial (for instance, for the polynomial 4x² + 7xyz, the degree is 3 because of the last term).

• If a polynomial isn't just a constant and if each term has at most a variable to the first power (like 4x - 2 or 3y), then it is a first-degree polynomial (also called a linear polynomial).
• If a polynomial's highest degree is two, it is a quadratic (or second-degree) polynomial (example: 4x² + 3x + 7).
• If a polynomial has more than one variable, then its degree is the sum of the exponents of the highest-degree term. For example, the polynomial 2xy² -3xy + 6x - 2 has degree 3 (the sum of the xy² exponents, 1 + 2).

equation - An equation is a mathematical statement that contains an equal sign, like ax + b = c.

exponent - An exponent is a power that a number is raised to. For example, in 2³, the exponent is 3.

expression - An algebraic expression consists of one or more variables, constants, and operations, like 3x-4. Each part of an expression that is added or subtracted is called a term For example, the expression 4x²-2x+7 has three terms.

factor - The factor of a number is a number that divides that number exactly. For example, the factors of 6 are 1, 2, 3 and 6.

formula - A formula shows a mathematical relationship between expressions.

fraction - A fraction is a part of a whole, like a half, a third, a quarter, etc. For example, half of an apple is a fraction of an apple. The top number in a fraction is called the numerator; the bottom number in a fraction is called the denominator.

inequality - An inequality is a mathematical expression that contains an inequality symbol. The inequality symbols are :

< less than (1<2)
> greater than (2>1)
≤ less than or equal to
≥ greater than or equal to
≠ not equal to (1≠2).

integer - The integers are the numbers ..., -3, -2, -1, 0, 1, 2, ....

inverse (addition) - The inverse property of addition states that for every number a, a + (-a) = 0 (zero).

inverse (multiplication) - The inverse property of multiplication states that for every non-zero number a, a times (1/a) = 1.

matrix -

n^th -

operation - An operation is a rule for taking one or two numbers as inputs and producing a number as an output. Some arithmetic operations are multiplication, division, addition, and subtraction.

polynomial - A polynomial is a sum or difference of terms; each term is:

• a constant (for example, 5)
• a constant times a variable (for example, 3x)
• a constant times the variable to a positive integer power (for example, 2x²)
• a constant times the product of variables to positive integer powers (for example, 2x³y).

prime number - A prime number is a positive number that has exactly two factors, 1 and itself. Alternatively, you can think of a prime number as a number greater than one that is not the product of smaller numbers. For example, 13 is a prime number because it can only be divided evenly by 1 and 13. For another example, 14 is not a prime number because it can be divided evenly by 1, 2, 7, and 14. The number one is not a prime number because it has only one factor, 1 itself.

quadratic equation - A quadratic equation is an equation that has a second-degree term and no higher terms. A second-degree term is a variable raised to the second power, like x², or the product of exactly two variables, like x and y.

When you graph a quadratic equation in one variable, like y = ax² + bx + c, you get a parabola, and the solutions to the quadratic equation represent the points where the parabola crosses the x-axis.

quadratic formula - The quadratic formula is a formula that gives you a solution to the quadratic equation ax² + bx + c = 0. The quadratic formula is obtained by solving the general quadratic equation.

radical - A radical is a symbol √ that is used to indicate the square root or n^th root of a number.

root - An n^th root of a number is a number that, when multiplied by itself n times, results in that number. For example, the number 4 is a square root of 16 because 4 x 4 equals 16. The number 2 is a cube root of 8 because 2 x 2 x 2 equals 8.

solve - When you solve an equation or a problem, you find solutions for it.

square root - The square roots of a number n are the numbers s such that s²=n. For example, the square roots of 4 are 2 and -2; the square roots of 9 are 3 and -3.

symbol - A symbol is a mark or sign that stands for something else. For example, the symbol ÷ means divide.

system of equations - A system of equations is two or more independent equations that are solved together. For example, the system of equations: x + y = 3 and x - y = 1 has a solution of x=2 and y=1.

terms - In an expression or equation, terms are numbers, variables, or numbers with variables. For example, the expression 3x has one term, the expression 4x² + 7 has two terms.

variable - A variable is an unknown or placeholder in an algebraic expression. For example, in the expression 2x+y, x and y are variables.

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