How to Add Polynomial Expressions: A Step-by-Step Guide
Quick Answer
To add polynomial expressions like (3x² - 2) + (11 - 5x), combine like terms. The result is 3x² - 5x + 9. Always check your signs and group similar terms for accuracy.
Adding polynomial expressions is a fundamental skill in algebra that can help you solve many mathematical problems. Let’s break down how to add two polynomials step by step, using the example of (3x² - 2) + (11 - 5x).
### Step 1: Write Out the Expression
First, rewrite the expression clearly. This helps prevent mistakes. Start with:
$$ (3x^2 - 2) + (11 - 5x) $$
### Step 2: Remove Parentheses
In our case, there are no additional operations needed inside the parentheses, so we can simply write:
$$ 3x^2 - 2 + 11 - 5x $$
### Step 3: Group Like Terms
Now, we need to group the like terms together. Like terms are terms that have the same variable raised to the same power. In our expression, we have:
- The $x^2$ term: **3x²**
- The $x$ term: **-5x**
- The constant terms: **-2** and **11**
### Step 4: Combine the Like Terms
Now, let’s combine the like terms:
- For the $x^2$ term: we only have **3x²**.
- For the $x$ term: we have **-5x**.
- For the constants: combine **-2** and **11**:
$$ -2 + 11 = 9 $$
So when we combine all these, we get:
$$ 3x^2 - 5x + 9 $$
### Final Result
Thus, the final answer to our polynomial addition is:
$$ 3x^2 - 5x + 9 $$
### Common Mistakes
One common mistake is to mismanage the signs when combining the constant terms or the coefficient of the $x$ term. In this case, if you selected **3x² + 5x - 9**, you had errors in both the sign of the $x$ term and the constant. Always double-check your signs!
### Real-World Application
Understanding how to add polynomial expressions is not just for homework. It’s used in various fields, such as physics for motion equations, economics for cost functions, and even computer science for algorithm design. By mastering this skill, you’re building a strong foundation for future math courses and real-world applications.
Remember, practice is key! Try adding different polynomial expressions and check your work to become more confident in your skills. You can find more practice problems and resources in the equations section of our site.
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