Coefficient
Pronunciation: /ˌkoʊ.əˈfɪ.ʃənt/ Explain
3x^{3} + 2x^{2}  4x  1
 Figure 1: Coefficients 

A coefficient is a number multiplied by
one or more variables.^{[2][3]} In the
term
3x, the coefficient is 3.
In figure 1, the coefficients are red. The coefficients in figure 1 are
(3, 2, 4, 1). A variable
without a coefficient has an implied coefficient of
1 (x^{3}
= 1·x^{3}).
In the expression x^{2} + 5, the
term containing x^{2} has an implied
coefficient of 1. Applying the
property of multiplying by 1
to the term gives
x^{2} = 1·x^{2}.

References
 McAdams, David E.. All Math Words Dictionary, coefficient. 2nd Classroom edition 201501084799968. pg 35. Life is a Story Problem LLC. January 8, 2015. Buy the book
 Keigwin, H. W.. Principles of Elementary Algebra. pg 5. www.archive.org. Ginn & Company. 1886. Last Accessed 6/25/2018. http://www.archive.org/stream/principlesofelem00dupurich#page/5/mode/1up/search/coefficient. Buy the book
 Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry. pg 17. www.archive.org. International Textbook Company. January 1963. Last Accessed 6/25/2018. http://www.archive.org/stream/algebraandtrigon033520mbp#page/n18/mode/1up. Buy the book
More Information
 McAdams, David E.. Term. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 6/27/2018. https://www.allmathwords.org/en/t/term.html.
 McAdams, David E.. Polynomial. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 3/28/2019. https://www.allmathwords.org/en/p/polynomial.html.
Cite this article as:
McAdams, David E. Coefficient. 4/13/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/c/coefficient.html.
Revision History
3/5/2019: Added vocabulary link. (
McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (
McAdams, David E.)
6/25/2018: Removed broken links, updated license, implemented new markup, updated GeoGebra apps. (
McAdams, David E.)
1/4/2010: Added "References". (
McAdams, David E.)
1/29/2009: Added text on implied coefficient of 1. (
McAdams, David E.)
6/1/2008: Initial version. (
McAdams, David E.)