Adding Polynomials: A StepbyStep 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:

Identify like terms:
 p3 terms: 3p3 and p3
 p2 terms: 5p2 and 8p2
 p terms: 2p and 15p

Combine the coefficients of like terms:
 3p3 + (p3) = 4p3
 5p2 + (8p2) = 3p2
 2p + (15p) = 17p

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