Leading Coefficient
The number in front of the term with the largest degree in a polynomial.
The leading coefficient of a polynomial is the coefficient of the term with the highest power, or degree, in the polynomial. For example, in the polynomial 3x^2 + 2x – 5, the leading coefficient is 3 because the term with the highest power, 3x^2, has a coefficient of 3.
The leading coefficient can help us determine important information about the polynomial, such as its end behavior. If the leading coefficient is positive, the graph of the polynomial will increase without bound as x approaches positive or negative infinity. If the leading coefficient is negative, the graph of the polynomial will decrease without bound as x approaches positive or negative infinity.
Additionally, the leading coefficient is important when factoring polynomials. In some cases, it can help us identify common factors or use the quadratic formula to find the roots of the polynomial.
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