Leading Coefficient
The number in front of the term with the largest degree in a polynomial.
The leading coefficient is the coefficient of the term with the highest degree in a polynomial. In other words, it is the coefficient of the term with the greatest exponent in the polynomial. For example, in the polynomial 5x^3 + 2x^2 – 7x + 4, the leading coefficient is 5 because it is the coefficient of the term with the highest degree (x^3).
The leading coefficient is important in polynomial equations because it determines the end behavior of the function. If the leading coefficient is positive, then as the input x approaches positive or negative infinity, the output of the function f(x) also approaches positive infinity. On the other hand, if the leading coefficient is negative, then as the input x approaches positive or negative infinity, the output of the function f(x) approaches negative infinity.
Additionally, in order to find roots or zeros of a polynomial, it is often helpful to use the leading coefficient to determine the possible rational roots or zeros of the function. The possible rational roots are given by the factors of the constant term divided by the factors of the leading coefficient.
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