7th grade Q2 (old curriculum)

Classify polynomials

How do you classify polynomials according to degree and number of terms?

Polynomials can be classified based on two main criteria:

Degree (the highest power of the variable)
Number of terms

1. Classification by Degree

The degree of a polynomial is the highest power (exponent) of the variable in the expression. Here’s how polynomials are classified according to their degree:

Degree 0: A polynomial with no variable part (a constant).

Example: 5
Name: Constant polynomial

Degree 1: The highest power of the variable is 1.

Example: $3 x + 2$
Name: Linear polynomial

Degree 2: The highest power of the variable is 2.

Example: $x^{2} + 4 x + 3$
Name: Quadratic polynomial

Degree 3: The highest power of the variable is 3.

Example: $2 x^{3} + 3 x^{2} + x$
Name: Cubic polynomial

Degree 4: The highest power of the variable is 4.

Example: $x^{4} - 2 x^{2} + x - 5$
Name: Quartic polynomial

Degree 5: The highest power of the variable is 5.

Example: $x^{5} - 2 x^{4} + 3 x$
Name: Quintic polynomial

For degrees higher than 5, we generally refer to them by their degree number (e.g., "degree 6 polynomial").

2. Classification by Number of Terms

The number of terms refers to how many terms the polynomial has. The terms are separated by addition or subtraction signs.

Monomial: A polynomial with one term.

Example: $2 x, 3 x^{2}, 3 x 2, 7 x$ or $- 5$
Name: Monomial

Binomial: A polynomial with two terms.

Example: $x^{2} - 4$ or $3 x + 2$
Name: Binomial

Trinomial: A polynomial with three terms.

Example: $x^{2} + 3 x + 2$
Name: Trinomial

Polynomial: A general term for an algebraic expression with more than three terms.

Example: $x^{3} + 4 x^{2} + x + 5$
Name: Polynomial (or specifically cubic polynomial in this case, according to its degree)

Combining Degree and Number of Terms

Polynomials can also be described using both their degree and the number of terms. Here are some examples:

Linear binomial: A degree 1 polynomial with two terms.

Example: $3 x + 4$

Quadratic trinomial: A degree 2 polynomial with three terms.

Example: $x^{2} + 2 x + 1$

Cubic monomial: A degree 3 polynomial with one term.

Example: $2 x^{3}$

Quartic polynomial: A degree 4 polynomial with multiple terms (but no specific number of terms is indicated).

Example: $x^{4} + 3 x^{3} + x^{2} - 5$

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Activity Set 1