Polynomial Basics: Degree, Terms, and Operations

A Polynomial is an expression consisting of variables and coefficients involving only addition, subtraction, multiplication, and non-negative integer exponents.

Key Vocabulary

Monomial: A polynomial with one term (e.g., $3x^2$).
Binomial: A polynomial with two terms (e.g., $x + 5$).
Trinomial: A polynomial with three terms (e.g., $x^2 + 2x + 1$).
Degree: The highest exponent of the variable in the polynomial.
Like Terms: Terms that have the same variable raised to the same power (e.g., $2x^2$ and $-5x^2$).

Operations: Adding and Subtracting

To add or subtract polynomials, you simply Combine Like Terms.

Standard Form:
Write the polynomial with terms in descending order of their degree (highest exponent first).

Step-by-Step Example

Simplify the expression:

$$(3x^2 - 5x + 2) - (x^2 + 2x - 4)$$

Step 1: Distribute the negative sign
The second parenthesis has a minus sign in front, so flip the signs of all terms inside.

$$3x^2 - 5x + 2 - x^2 - 2x + 4$$

Step 2: Group Like Terms

$x^2$ terms: $3x^2 - x^2$
$x$ terms: $-5x - 2x$
Constant terms: $2 + 4$

Step 3: Combine

$3x^2 - 1x^2 = 2x^2$
$-5x - 2x = -7x$
$2 + 4 = 6$

Solution:

$$2x^2 - 7x + 6$$

Why reading isn’t enough

Identifying like terms correctly is essential for algebra. Errors often occur when subtracting polynomials because students forget to distribute the negative sign to every term in the second group.

Weekzen provides endless practice on combining like terms and polynomial operations. We ensure you master the basics before moving on to more complex topics like factoring.