what is factoring in math

Factoring in math is the process of breaking down an expression into a product of simpler expressions called factors. It is like finding the numbers or expressions you multiply together to get the original expression. For example, if you have an expression like 2y + 6, factoring involves identifying what can be multiplied to produce it. Since both 2y and 6 share a common factor of 2, you can factor it as 2(y + 3). Factoring is essentially the reverse of expanding. For numbers, factors are numbers that divide a given number exactly without leaving a remainder. For algebraic expressions, factoring is identifying simpler expressions multiplied to form the original polynomial or algebraic expression. In summary, factoring means expressing a number or algebraic expression as a product of its factors, which simplifies the expression or helps in solving equations. For instance, factoring a quadratic expression like x2+5x+6x^2+5x+6x2+5x+6 would yield (x+2)(x+3)(x+2)(x+3)(x+2)(x+3), meaning the expression can be written as the multiplication of (x+2)(x+2)(x+2) and (x+3)(x+3)(x+3). Factoring is widely used in algebra for simplifying expressions, solving equations, and finding common factors across terms. It involves concepts such as the greatest common factor or special polynomial identities (difference of squares, sum of cubes, etc.).