Let's Meet Polynomials Discover the equations that give algebra its voice.

Parts of a Polynomial

Illustration of polynomial parts

Pattern in every term

Each arrow shows one part. Every term fits: coefficient × variable\(^{\text{exponent}}\).

Key Points:

  • Coefficient – number multiplied by the variable.
  • Variable – letter that can change value.
  • Exponent – small power on the variable.
  • Operator – + or – sign joining terms.
  • Constant – term without a variable.

What is a Polynomial?

Polynomial

A polynomial in one variable is a sum or difference of terms \(a x^{n}\) where \(a\) is any real number and \(n\) is a whole number \(0,1,2,\dots\).

1, 2, or 3 Terms?

https://asset.sparkl.ac/pb/sparkl-vector-images/img_ncert/cyB1XNeNb1s1OpOzWebpskhocNbc9FDjPXBJat8U.png

Types by Number of Terms

Count the unlike terms in an expression to name it correctly.

Key Points:

  • Monomial → 1 term, e.g. \(5x\)
  • Binomial → 2 terms, e.g. \(3x+2\)
  • Trinomial → 3 terms, e.g. \(x^{2}+2x+1\)

Sort the Expressions

Drag each algebraic expression into its correct basket: monomial, binomial, or trinomial.

Draggable Items

\(5x\)
\(3y + 2\)
\(4a^{2}-7a+1\)

Drop Zones

Monomial

Binomial

Trinomial

Tip:

Count unlike terms: 1 → monomial, 2 → binomial, 3 → trinomial.

Degree of a Polynomial

Degree

The degree is the highest power (largest exponent) of the variable in a polynomial.

Key Characteristics:

  • Highest power decides the degree.
  • Degree 1 → Linear polynomial.
  • Degree 2 → Quadratic polynomial.
  • Degree 3 → Cubic polynomial.

Example:

\(5x^2 + 3x + 1\) has highest exponent \(2\); therefore, it is quadratic.

Check Your Pick

Question

Formative assessment: Which expression below is NOT a polynomial in \(x\)?

1
\(2x^{2}-5x+1\)
2
\(3x^{3}+4\)
3
\(x^{-1}+2\)
4
7

Hint:

A polynomial has only whole-number exponents on \(x\).

Key Takeaways

A polynomial is a sum of terms \(a x^{n}\) where \(n\) is a whole number.

Each term has a coefficient, variable, exponent, and sometimes a constant part.

By term count, we label them monomial, binomial, or trinomial.

The highest exponent, called degree, classifies polynomials as linear, quadratic, or cubic.

Polynomial visual

Thank You!

We hope you found this lesson informative and engaging.