Polynomial Operations

What’s a Polynomial?

An expression with variables and coefficients, using only:

• Addition and subtraction
• Multiplication
• Non-negative integer exponents (0, 1, 2, 3, …)

Degree

The degree is the highest exponent in the polynomial.

What’s NOT a Polynomial

• $\frac{1}{x}$ — negative exponent ($x^{-1}$)
• $\sqrt{x}$ — fractional exponent ($x^{1/2}$)
• $2^x$ — variable in the exponent

Adding and Subtracting

Combine like terms (same variable and exponent).

$(3x^2 + 2x) + (5x^2 - x) = 8x^2 + x$

Multiplying

Distribute each term to every term in the other polynomial.