%2B(3x%5E2-10x%2B4).jpeg "(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.