-5x-2x%5E(2)-8-8x%5E(2)-7x-9-3%2B7x%5E(2)-2x.jpeg "(vii) 5x-2x^(2)-8 8x^(2)-7x-9 3+7x^(2)-2x")
Simplifying and Combining Polynomials
This article will explore how to simplify and combine the following polynomials:
- 5x - 2x^(2) - 8
- 8x^(2) - 7x - 9
- 3 + 7x^(2) - 2x
Understanding Polynomials
Polynomials are mathematical expressions consisting of variables and constants combined using addition, subtraction, and multiplication. Each term in a polynomial is a product of a constant and one or more variables raised to non-negative integer powers.
Simplifying Polynomials
Simplifying polynomials involves combining like terms. Like terms are terms with the same variable(s) raised to the same power.
Here's how we simplify each polynomial:
1. 5x - 2x^(2) - 8
This polynomial is already in its simplest form. We can rearrange the terms for easier reading:
-2x^(2) + 5x - 8
2. 8x^(2) - 7x - 9
This polynomial is also in its simplest form.
3. 3 + 7x^(2) - 2x
Rearranging terms for clarity:
7x^(2) - 2x + 3
Combining Polynomials
To combine polynomials, we simply add or subtract their like terms.
Let's combine the three simplified polynomials:
(-2x^(2) + 5x - 8) + (8x^(2) - 7x - 9) + (7x^(2) - 2x + 3)
- Combine the x^(2) terms: -2x^(2) + 8x^(2) + 7x^(2) = 13x^(2)
- Combine the x terms: 5x - 7x - 2x = -4x
- Combine the constant terms: -8 - 9 + 3 = -14
The combined polynomial is:
13x^(2) - 4x - 14
Conclusion
By understanding the concepts of like terms and simplification, we can easily combine polynomials to create a single, simplified expression. This process is fundamental in various mathematical operations and applications.