Algebraic Identities and Factorization An algebraic identity is a statement that is true for all values of the variables involved. For example, the iden...
Algebraic Identities and Factorization
An algebraic identity is a statement that is true for all values of the variables involved. For example, the identity (a + b)^2 = a^2 + 2ab + b^2 is true for all real numbers a and b.
An algebraic factor is a factor of a polynomial that is not zero. For example, the factors of the polynomial x^2 - 4 are (x + 2) and (x - 2).
The factorization theorem states that a polynomial of degree n can be expressed as a product of n linear factors. For example, the polynomial x^2 - 4 can be expressed as (x + 2)(x - 2).
Examples:
The identity (a + b)^2 = a^2 + 2ab + b^2 is a fundamental identity in algebra.
The factors of the polynomial x^2 - 9 are (x + 3)(x - 3).
The factorization theorem can be used to express the polynomial x^2 - 9 as (x + 3)(x - 3)