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(4x^3-5x^2+3x-8)+(2x^3-2x^2+6x+12)

2 min read Jun 16, 2024
(4x^3-5x^2+3x-8)+(2x^3-2x^2+6x+12)

Adding Polynomials: A Step-by-Step Guide

This article will walk you through the process of adding the polynomials (4x^3-5x^2+3x-8) and (2x^3-2x^2+6x+12).

Understanding Polynomials

Polynomials are expressions consisting of variables and coefficients, combined using addition, subtraction, and multiplication. They can be arranged in descending order of their exponents.

Adding Polynomials

Adding polynomials involves combining like terms. Like terms have the same variable and exponent. Here's how we add the given polynomials:

  1. Write the polynomials vertically, aligning like terms:
  4x^3 - 5x^2 + 3x - 8
+ 2x^3 - 2x^2 + 6x + 12
--------------------
  1. Add the coefficients of each like term:
  4x^3 - 5x^2 + 3x - 8
+ 2x^3 - 2x^2 + 6x + 12
--------------------
  6x^3 - 7x^2 + 9x + 4
  1. The sum of the polynomials is:

(4x^3-5x^2+3x-8)+(2x^3-2x^2+6x+12) = 6x^3 - 7x^2 + 9x + 4

Key Points to Remember

  • Only combine like terms. You cannot add terms with different variables or exponents.
  • Simplify the expression. Make sure the final answer is in its simplest form, combining any remaining like terms.

By following these steps, you can confidently add any two polynomials. Remember, practice makes perfect!

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