Algebra & Equations Vocabulary

a symbol representing an unknown or changeable quantity

“Let x be the variable representing the unknown price.”

Origin: Latin variabilis `changeable`, from variare `to change`

a numerical factor multiplying a variable

“In 3x², the coefficient is 3.”

Origin: New Latin coefficiens, from Latin co- `together` + efficere `to accomplish`

an expression of variables and coefficients using only addition, subtraction, and multiplication

“x³ + 2x² - 5x + 1 is a cubic polynomial.”

Origin: Greek poly `many` + Latin nomen `name, term`

involving the second power of a variable

“The quadratic formula solves any equation of the form ax² + bx + c = 0.”

Origin: Latin quadratus `square`, from quattuor `four` (four-sided figure)

expressing a number or expression as a product of its factors

“The factorization of x² - 9 is (x+3)(x-3).”

Origin: Latin factor `doer, maker` + -ization

a rectangular array of numbers arranged in rows and columns

“Matrix multiplication is not commutative.”

Origin: Latin matrix `womb, source`, from mater `mother`

a scalar value computed from a square matrix

“A matrix is invertible only if its determinant is non-zero.”

Origin: Latin determinare `to limit, fix`, from de- + terminus `boundary`

a scalar by which an eigenvector is scaled under a linear transformation

“The eigenvalues reveal the matrix's fundamental scaling behaviors.”

Origin: German eigen `own, characteristic` + English value

an element that combines with another to produce an identity element

“The inverse of 5 under multiplication is 1/5.”

Origin: Latin inversus `turned upside down`, from invertere `to turn inside out`

an element that leaves other elements unchanged under an operation

“Zero is the additive identity; one is the multiplicative identity.”

Origin: Latin identitas `sameness`, from idem `same`