Leading Coefficient
The number in front of the term with the largest degree in a polynomial.
In algebra, a polynomial is an expression consisting of variables and coefficients combined using arithmetic operations like addition, subtraction, multiplication, and division. The leading coefficient of a polynomial is the coefficient of the term with the highest degree.
For example, let’s consider the polynomial:
4x^3 + 2x^2 – 3x + 1
The leading term in this polynomial is 4x^3, and the coefficient of this term is 4. Therefore, the leading coefficient of this polynomial is 4.
The leading coefficient of a polynomial plays an important role in determining the end behavior of the graph of the function defined by the polynomial. For example, if the leading coefficient is positive, the graph of the polynomial will have both ends pointing upwards. On the other hand, if the leading coefficient is negative, the graph of the polynomial will have both ends pointing downwards.
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