Quick answer

Add and subtract combine like terms (coefficients only). Multiply and divide follow different exponent rules and are not handled by this tool.

Formula

  • This site focuses on (P ± Q)(x) via coefficient alignment.

Introduction

This article situates add and subtract inside the wider topic of polynomial operations. The Adding and Subtracting Polynomials Calculator handles addition and subtraction only.

Knowing which operation a problem asks for prevents applying multiply rules during a subtraction exercise.

Core operations

Addition and subtraction keep the expression in polynomial form with whole-number exponents. You merge coefficients on matching powers.

Definitions and vocabulary start in what polynomials are; without that base, operation names blur together.

Multiplication raises degrees and adds exponents; division can produce remainders or fractions, which are not covered here.

Quick comparison

  • Add/subtract: same exponent, combine coefficients.
  • Multiply: exponents add; coefficients multiply.
  • Divide: not the focus of this calculator.

On a test, read the symbol between polynomials carefully. A plus means align and add; a minus means negate Q completely, then add.

For sign and order issues, read polynomial addition vs subtraction next to contrast the two operations you will use most on this site.

Step-by-step guide

  1. Classify the problem. Are you combining two polynomials with +/−, or multiplying/dividing? Do not mix rules.
  2. Pick the correct procedure. Add/subtract: standard form, align powers, combine coefficients. Multiply: use the distributive property or grid methods from class, not this tool.
  3. Simplify the result. After ±, merge like terms and write standard form.
  4. Use the tool when appropriate. Enter P and Q in polynomial calculator only for addition or subtraction tasks.

Example: same pair, different operations

Let P(x) = x + 1 and Q(x) = x². Then P + Q = x² + x + 1 (degree 2). Coefficients on x² and x and constant were added separately.

Multiplication would give P·Q = x³ + x², so the exponents differ, different meaning.

Use Add mode in the polynomial calculator for the sum only; do not expect multiply results from this calculator.