(3x^4-2x^6+x^3-x+5)+(x^6-3x^2+4x-1)

3 min read Jun 16, 2024

Adding Polynomials: A Step-by-Step Guide

This article will guide you through the process of adding the polynomials (3x^4-2x^6+x^3-x+5) and (x^6-3x^2+4x-1). We will break down the steps and explain the concepts involved.

Understanding Polynomials

A polynomial is an expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication. Each term in a polynomial is a product of a coefficient and one or more variables raised to non-negative integer powers.

Adding Polynomials

To add polynomials, we follow these simple steps:

Identify Like Terms: Identify terms with the same variable and exponent. For example, 3x^4 and -2x^6 are like terms because they both have x raised to the same power.
Combine Like Terms: Add the coefficients of like terms together, keeping the variable and exponent unchanged.
Simplify: Combine the resulting terms to obtain the final polynomial.

Applying the Steps to our Example

Let's apply these steps to our polynomials: (3x^4-2x^6+x^3-x+5) and (x^6-3x^2+4x-1).

Identify Like Terms:
- x^6: -2x^6 and x^6
- x^4: 3x^4
- x^3: x^3
- x^2: -3x^2
- x: -x and 4x
- Constant: 5 and -1
Combine Like Terms:
- x^6: -2x^6 + x^6 = -x^6
- x^4: 3x^4
- x^3: x^3
- x^2: -3x^2
- x: -x + 4x = 3x
- Constant: 5 - 1 = 4
Simplify: Combine the resulting terms: -x^6 + 3x^4 + x^3 - 3x^2 + 3x + 4

Conclusion

Therefore, the sum of the polynomials (3x^4-2x^6+x^3-x+5) and (x^6-3x^2+4x-1) is -x^6 + 3x^4 + x^3 - 3x^2 + 3x + 4. By following the steps of identifying, combining, and simplifying like terms, you can successfully add any two polynomials.