The leading term of a polynomial is the term that contains the highest power of the variable. In a polynomial, the terms are typically arranged in descending order based on the exponent of the variable (commonly ‘x’). The leading term is significant because it helps to determine the behavior of the polynomial as the value of the variable approaches infinity or negative infinity.
For example, consider the polynomial:
f(x) = 4x^3 + 2x^2 – 5x + 7
In this case, the leading term is 4x^3, since ‘3’ is the highest exponent of ‘x’ in the polynomial. The coefficient of the leading term, which is ‘4’ in this instance, also plays an important role in determining the direction of the graph as it stretches towards infinity.
Understanding the leading term is crucial when analyzing the polynomial’s end behavior and its overall shape in a graphical context.