Interactive Polynomial Vocabulary Activity

Using the drop-down selectors, classify the polynomial and identify its leading coefficient and constant.


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Learn the Vocabulary

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.

Name Degree Standard Form Example Notes
Constant 0 a -6 A constant expression is non-variable, so it has no coefficients. You could say the leading coefficient is 0.
Linear 1 ax+b 4x-6
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?