%2B(5x%5E3%2B3x%5E2-2x-1).jpeg "(-8x^3+7x^2+x-9)+(5x^3+3x^2-2x-1)")
Simplifying Polynomials: A Step-by-Step Guide
This article will guide you through simplifying the following polynomial expression:
(-8x³ + 7x² + x - 9) + (5x³ + 3x² - 2x - 1)
Understanding the Basics
Polynomials are algebraic expressions with multiple terms, each consisting of a coefficient and a variable raised to a non-negative integer power. To simplify polynomials, we need to combine like terms.
Combining Like Terms
1. Identify Like Terms:
Like terms are terms that have the same variable raised to the same power. In our expression, we have:
- x³ terms: -8x³ and 5x³
- x² terms: 7x² and 3x²
- x terms: x and -2x
- Constant terms: -9 and -1
2. Combine Coefficients:
Add the coefficients of each set of like terms:
- -8x³ + 5x³ = -3x³
- 7x² + 3x² = 10x²
- x - 2x = -x
- -9 - 1 = -10
3. Write the Simplified Expression:
Putting it all together, the simplified expression is:
-3x³ + 10x² - x - 10
Conclusion
By following these steps, we have successfully simplified the given polynomial expression. This process of combining like terms is crucial for manipulating and solving polynomial equations and expressions.