A coefficient is a numerical or constant factor that multiplies a variable in a term of an algebraic expression or equation. For example, in the term $5x^2$, 5 is the coefficient.
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In polynomial functions, coefficients determine the shape and position of the graph.
The leading coefficient is the coefficient of the term with the highest degree in a polynomial.
In a polynomial like $3x^3 + 2x^2 - x + 7$, 3, 2, -1, and 7 are all coefficients.
Coefficients can also be fractions or irrational numbers.
Review Questions
What is the coefficient of $x$ in the term $-4x$?
In the polynomial $6x^4 - 3x^2 + x - 8$, what is the leading coefficient?
How do coefficients affect the shape of a polynomial's graph?
Related terms
Polynomial: An algebraic expression consisting of terms which are sums and/or differences of variables raised to non-negative integer powers and multiplied by coefficients.
Leading Coefficient: The coefficient of the term with the highest degree in a polynomial.
Zero of a Polynomial: A value for which a given polynomial evaluates to zero; also known as root or solution.