Leading term

Definition

The leading term of a polynomial is the term with the highest power of the variable. It determines the end behavior of the polynomial function.

5 Must Know Facts For Your Next Test

1. The leading term is essential for understanding the graph's end behavior.
2. In a polynomial, the leading term includes both the highest degree variable and its coefficient.
3. The leading coefficient is part of the leading term and significantly affects the graph's steepness.
4. For polynomials written in standard form, the leading term appears first.
5. The degree of a polynomial is determined by the exponent in its leading term.

Review Questions

• What is the leading term in the polynomial $3x^4 - 5x^3 + 2x - 7$?
• How does the leading coefficient affect a polynomial graph’s steepness?
• In what form should a polynomial be written to easily identify its leading term?

Related terms

Polynomial:

A mathematical expression consisting of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication.

Leading Coefficient:

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

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