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

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

Simplifying Polynomial Expressions: (x^2 + x + 5) + (3x^2 - 10x + 4)

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

Understanding the Problem

The expression involves two polynomials:

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

We are asked to add these two polynomials.

Simplifying the Expression

1. Remove the Parentheses:

Since we are adding the two polynomials, the parentheses are unnecessary. We can simply rewrite the expression as:

x^2 + x + 5 + 3x^2 - 10x + 4

2. Combine Like Terms:

  • x^2 terms: x^2 + 3x^2 = 4x^2
  • x terms: x - 10x = -9x
  • Constant terms: 5 + 4 = 9

3. Write the Simplified Expression:

Combining the like terms, we get the simplified expression:

4x^2 - 9x + 9

Conclusion

Therefore, the simplified form of the expression (x^2 + x + 5) + (3x^2 - 10x + 4) is 4x^2 - 9x + 9. This process demonstrates the fundamental principles of combining polynomials by identifying and combining like terms.

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