(3x^2+4x-1)+(-2x^2-3x+2) Find The Sum

Jasonbradley

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Jun 16, 2024

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Finding the Sum of Polynomials: (3x^2+4x-1)+(-2x^2-3x+2)

This problem involves adding two polynomials. Let's break it down step-by-step:

Understanding Polynomials

A polynomial is an expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication, but never division by a variable.

Key terms:

• Variable: A symbol representing an unknown quantity (e.g., 'x').
• Coefficient: A number multiplying a variable (e.g., '3' in 3x^2).
• Term: A single variable, coefficient, or their product (e.g., '4x').

Adding Polynomials

To add polynomials, we combine like terms. Like terms have the same variable raised to the same power.

Steps:

1. Identify like terms:

   • 3x^2 and -2x^2 are like terms
   • 4x and -3x are like terms
   • -1 and 2 are like terms

2. Combine like terms by adding their coefficients:

   • (3x^2 - 2x^2) + (4x - 3x) + (-1 + 2)

3. Simplify the expression:

   • x^2 + x + 1

Solution

Therefore, the sum of (3x^2 + 4x - 1) and (-2x^2 - 3x + 2) is x^2 + x + 1.