How do we classify the expression 7x3 + 2x2 + 9x + 1 as a monomial, binomial, trinomial, or polynomial?

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The expression 7x3 + 2x2 + 9x + 1 can be classified based on the number of terms it contains:

  • Monomial: An expression with only one term. For example, 5x2 is a monomial.
  • Binomial: An expression with exactly two terms. An example would be 3x + 4.
  • Trinomial: This is an expression that consists of three terms. For instance, x2 + 2x + 1 is a trinomial.
  • Polynomial: A polynomial is an expression containing one or more terms, and it can have any number of terms.

Now, in our case, the expression 7x3 + 2x2 + 9x + 1 has four terms:

  1. 7x3
  2. 2x2
  3. 9x
  4. 1

Since the expression features more than three terms, it does not fit into the categories of monomial, binomial, or trinomial. Therefore, we classify the expression as a polynomial.

In summary, the expression 7x3 + 2x2 + 9x + 1 is a polynomial with four terms.

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