A linear factor is a first-degree equation that is a building block of more complex and higher-order polynomials. Linear factors appear in the form of ax + b and cannot be factored further. Each linear factor represents a different line that, when combined with other linear factors, results in different types of functions with increasingly complex graphical representations. Linear factors are univariate, meaning they only have one variable that affects the function, typically designated as x and corresponding to movement on the x-axis. The slope of a linear factor is the coefficient assigned to the variable in the form y = ax + b, and the constant in a linear equation is the b in the form y = ax + b.

Linear factors are also used in finance to model the relationship between the return on an asset and the values of a limited number of factors. The key assumption of a linear factor model is that the residual for one assets return is uncorrelated with that of any other.

In algebra, a linear factor is a factor whose highest power of the variable is 1. For example, 3x + 2, x-4, -2x+3, etc. are linear factors. Quadratic expressions like 2x^2 - x are not linear factors.

Linear factors are also used in calculus to decompose rational expressions into partial fractions. When the denominator of the simplified expression contains distinct linear factors, it is likely that each of the original rational expressions, which were added or subtracted, had one of the linear factors as the denominator.