Leading term

Definition

The leading term of a polynomial is the term with the highest degree, which dictates the polynomial's end behavior. It consists of the leading coefficient and the variable raised to the highest power.

5 Must Know Facts For Your Next Test

1. The degree of the polynomial is determined by the exponent in the leading term.
2. The leading term affects the end behavior of the polynomial function.
3. In standard form, polynomials are written with terms in descending order of their degrees, making it easy to identify the leading term.
4. The sign of the leading coefficient influences whether the graph opens upwards or downwards for even-degree polynomials.
5. When adding or subtracting polynomials, combine like terms and then identify the new leading term.

Review Questions

• What is the leading term of $3x^4 + 2x^3 - x + 7$?
• How does changing the sign of a leading coefficient affect a polynomial's graph?
• If given a polynomial in non-standard form, how can you identify its leading term?

Related terms

Polynomial: An algebraic expression consisting of variables and coefficients, involving only addition, subtraction, multiplication, and non-negative integer exponents.

Degree: The highest power of the variable in a polynomial.

Leading Coefficient: The coefficient of the term with the highest degree in a polynomial.