The leading coefficient is the number that multiplies a variable to the highest degree in the expression. Because polynomials are arranged by degree from highest to lowest, the leading coefficient is the first number that appears in the expression, unless the coefficient is 1.
For example, in the polynomial 4x^3 + 2y^2 + 3x -1, the leading coefficient is 4 because 4x is raised to the third and highest degree. Rewriting the polynomial as 2y^2 + 3x + 4x^3 -1, while not changing the value of the expression, violates the convention of arranging polynomials in descending order of degree. For a polynomial such as x^2 + 2x + 4, the leading coefficient is 1 because the numeral 1 is omitted by convention from 1x^2.