Coefficient

Pronunciation: /ˌkoʊ.əˈfɪ.ʃənt/ Explain

3x3 + 2x2 - 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 (x3 = 1·x3). In the expression x2 + 5, the term containing x2 has an implied coefficient of 1. Applying the property of multiplying by 1 to the term gives x2 = 1·x2.

References

1. McAdams, David E.. All Math Words Dictionary, coefficient. 2nd Classroom edition 20150108-4799968. pg 35. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. 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
3. 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.)