2 min read Jun 17, 2024

Adding Polynomials: A Step-by-Step Guide

This article will walk you through the process of adding the polynomials (−3p3+5p2−2p) + (−p3−8p2−15p).

Understanding the Basics

Before we dive in, let's quickly recap what polynomials are:

  • Polynomials are expressions consisting of variables and coefficients, combined using addition, subtraction, and multiplication.
  • Terms in a polynomial are separated by addition or subtraction signs.
  • Like terms have the same variable and exponent.

Adding the Polynomials

To add polynomials, we simply combine like terms:

  1. Identify like terms:

    • p3 terms: -3p3 and -p3
    • p2 terms: 5p2 and -8p2
    • p terms: -2p and -15p
  2. Combine the coefficients of like terms:

    • -3p3 + (-p3) = -4p3
    • 5p2 + (-8p2) = -3p2
    • -2p + (-15p) = -17p
  3. Write the simplified polynomial:

    • (-3p3 + 5p2 - 2p) + (-p3 - 8p2 - 15p) = -4p3 - 3p2 - 17p


By following these simple steps, we have successfully added the given polynomials. Remember that the key is to identify and combine like terms. This process is fundamental in understanding and manipulating algebraic expressions.

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