(-6x^3-9x^2-10x+6)+(8x^4-5x^3+4x^2+9x+3)

Jasonbradley

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Jun 16, 2024

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Simplifying Polynomial Expressions

This article will guide you through simplifying the following polynomial expression:

(-6x^3 - 9x^2 - 10x + 6) + (8x^4 - 5x^3 + 4x^2 + 9x + 3)

Understanding the Process

Simplifying polynomial expressions involves combining like terms. Like terms are terms that have the same variable and exponent. For example, 3x^2 and -2x^2 are like terms because they both have the variable 'x' raised to the power of 2.

Step-by-Step Solution

1. Remove Parentheses: Since we are adding the two polynomials, the parentheses do not change the signs of the terms inside.

   (-6x^3 - 9x^2 - 10x + 6) + (8x^4 - 5x^3 + 4x^2 + 9x + 3) = -6x^3 - 9x^2 - 10x + 6 + 8x^4 - 5x^3 + 4x^2 + 9x + 3

2. Rearrange Terms: It's helpful to rearrange the terms to group like terms together.

   8x^4 - 6x^3 - 5x^3 - 9x^2 + 4x^2 - 10x + 9x + 6 + 3

3. Combine Like Terms: Combine the coefficients of the like terms.

   8x^4 - 11x^3 - 5x^2 - x + 9

Result

The simplified form of the polynomial expression is: 8x^4 - 11x^3 - 5x^2 - x + 9