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(x^4-3x^3+5x^2+x-4)-(x^3-4x^2-11x+10)

2 min read Jun 17, 2024
(x^4-3x^3+5x^2+x-4)-(x^3-4x^2-11x+10)

Simplifying Polynomial Expressions

This article will guide you through simplifying the polynomial expression: (x^4 - 3x^3 + 5x^2 + x - 4) - (x^3 - 4x^2 - 11x + 10).

Understanding the Problem

We are asked to subtract two polynomial expressions. To do this, we will follow these steps:

  1. Distribute the negative sign: The minus sign in front of the second set of parentheses means we multiply each term inside the parentheses by -1.
  2. Combine like terms: We identify terms with the same variable and exponent and combine their coefficients.

Simplifying the Expression

Let's apply the steps:

  1. Distribute the negative sign: (x^4 - 3x^3 + 5x^2 + x - 4) - (x^3 - 4x^2 - 11x + 10) = x^4 - 3x^3 + 5x^2 + x - 4 - x^3 + 4x^2 + 11x - 10

  2. Combine like terms: x^4 - 3x^3 - x^3 + 5x^2 + 4x^2 + x + 11x - 4 - 10 = x^4 - 4x^3 + 9x^2 + 12x - 14

Final Result

The simplified form of the given expression is x^4 - 4x^3 + 9x^2 + 12x - 14.

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