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What is the leading coefficient of a polynomial

1,076 views · Published 25 January 2013 · 5:16 · Indexed 23 September 2026

Channel: Brian McLogan · 2013 · Education

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👉 Learn how to determine the end behavior of the graph of a polynomial function. To do this we will first need to make sure we have the polynomial in standard form with descending powers. We will then identify the leading terms so that we can identify the leading coefficient and degree of the polynomial.  

The end behavior of a polynomial depends on the leading coefficient (the coefficient of the term with the greatest power) and the degree (the exponent of the term with the greatest power) of the polynomial. If the degree is even and the leading coefficient is positive, the graph of the polynomial rises left and rises right.  If the degree is even and the leading coefficient is negative, the graph of the polynomial falls left and falls right.  If the degree is odd and the leading coefficient is positive, the graph of the polynomial falls left and rises right.  If the degree is odd and the leading coefficient is negative, the graph of the polynomial rises left and falls right.

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Organized Videos:
✅End Behavior of Polynomial Functions
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMqQmihlAoPyCMZ2lwNKEAWa
✅How to Find the End Behavior From an Equation
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMpL6kXLtVJvJiXu4MPjSyzv
✅How to Find the End Behavior From a Graph
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMqJm89-2dxP5Lc9Rxo0arHj
✅End Behavior | Learn About
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMqJstbMyVsEy6iZDQL98Lap
✅How to Find the End Behavior From Factors
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMqd5cd9_KYlx7bnx2sFIDd_

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