leading coefficient
the number in the front of the expression in standard form
In mathematics, a polynomial is an expression consisting of variables and coefficients, which are combined using arithmetic operations of addition, subtraction, multiplication, and, in some cases, division. The leading coefficient of a polynomial refers to the coefficient of the term with the highest degree in the polynomial.
For example, in the polynomial 3x^4 + 2x^3 – 5x^2 + 6x – 1, the term with the highest degree of x is 3x^4, and the coefficient of this term is 3. Therefore, the leading coefficient of this polynomial is 3. The leading coefficient of a polynomial can be positive, negative, or zero.
The concept of the leading coefficient is important in polynomial algebra because it helps to determine the behavior of the polynomial as the variable x increases or decreases without bound. Specifically, the sign of the leading coefficient determines whether the polynomial opens up or opens down as x goes to infinity, and whether the polynomial has a maximum or a minimum value.
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