You have successfully completed 0 polynomials.
In the tables below, hover over any example to see a tooltip with the leading coefficient and constant term. Try to guess first!
Classification by Degree: The degree of a polynomial is its largest exponent. The degree will determine many properties of a polynomial, including how many roots it has and the shape of its graph. Thus it is helpful to name the common degrees.
|Constant||0||a||-6||A constant expression is non-variable, so it has no coefficients. You could say the leading coefficient is 0.|
|Quadratic||2||ax2+bx+c||3x2+4x-6||Why "quadratic" when quad means 4? Think of a square. It has 4 sides, but the expression of its area is represented by x2, or one side of the square raised to the second power.|
|Cubic||3||ax3+bx2+cx+d||3x2-x3-6+4x||This example is not in standard form. It is still cubic, with a leading coefficient of -1 and a constant term of -6|
|Quartic||4||ax4+bx3+cx2+dx+e||x4-x3+3x2+4x-6||In this example, the leading coefficient is the implied 1.|
|Quintic||5||ax5+bx4+cx3+dx2+ex+f||x5-x3||In this example, the missing constant term is considered 0.|
Classification by Terms: The number of terms a polynomial has may be helpful when determining appropriate methods of factoring and solving. Special techniques may be applied to 1-, 2-, or 3-term polynomials, so they are commonly referred by this classification.
|Name||Number of Terms||Example||Notes|
|Monomial||1||-5x3||Any degree polynomial may be a monomial, but a constant term MUST be a monomial.|
|Binomial||2||x3-27||Linear expressions can only be binomial or monomial.|
|Trinomial||3||5x2-3x-2||Quadratic expressions can be trinomial or smaller.|
|Polynomial||4 or more||x4-x3+3x2+4x-6||Can you infer the maximum number of terms given a polynomial's degree?|