In elementary algebra, a trinomial is a polynomial consisting of three terms or monomials.^[1]

1. ${\displaystyle 3x+5y+8z}$ with ${\displaystyle x,y,z}$ variables
2. ${\displaystyle 3t+9s^{2}+3y^{3}}$ with ${\displaystyle t,s,y}$ variables
3. ${\displaystyle 3ts+9t+5s}$ with ${\displaystyle t,s}$ variables
4. ${\displaystyle ax^{2}+bx+c}$, the quadratic polynomial in standard form with ${\displaystyle a,b,c}$ variables.^{[note 1]}
5. ${\displaystyle Ax^{a}y^{b}z^{c}+Bt+Cs}$ with ${\displaystyle x,y,z,t,s}$ variables, ${\displaystyle a,b,c}$ nonnegative integers and ${\displaystyle A,B,C}$ any constants.
6. ${\displaystyle Px^{a}+Qx^{b}+Rx^{c}}$ where ${\displaystyle x}$ is variable and constants ${\displaystyle a,b,c}$ are nonnegative integers and ${\displaystyle P,Q,R}$ any constants.

A trinomial equation is a polynomial equation involving three terms. An example is the equation ${\displaystyle x=q+x^{m}}$ studied by Johann Heinrich Lambert in the 18th century.^[2]