Unpacking College Algebra: Simplifying Expressions for Success

Let’s break down a classic algebra expression: x² + 11x + 30. If you’ve faced the College Algebra CLEP Prep Exam, you know—simplifying such expressions can feel daunting. So, grab a pencil, and let’s get to it together!

First off, what does it mean to simplify x² + 11x + 30? We're actually looking for a way to express this quadratic equation in its factored form. You might be thinking, “Why should I care about factoring?” Well, factoring is like finding the secret code behind the equation, making it easier to work with!

Here’s the thing: when we factor x² + 11x + 30, we’re searching for two numbers that multiply to 30 (the constant term) and add up to 11 (the coefficient of the x term). Those numbers are 6 and 5. So, we can express the equation as (x + 6)(x + 5).

Now, let’s distribute and double-check our work! When we expand (x + 6)(x + 5), we multiply each term as follows:

• x * x = x²,
• x * 5 = 5x,
• 6 * x = 6x,
• 6 * 5 = 30.

Putting it all together gives us x² + 5x + 6x + 30. When we combine like terms, we arrive back at x² + 11x + 30, confirming we’ve simplified it correctly.

Now, let’s tackle the multiple choice question, shall we? The question originally posed is: What is the result of x² + 11x + 30?

A. x² + 41
B. x² + 21x + 10
C. x² - 11x - 20
D. x² + 11x - 30

Drum roll, please... the correct answer is A: x² + 41. Just kidding! Actually, the tricky bit here is the options given. While we correctly factored and simplified x² + 11x + 30, the answer options didn’t reflect our findings accurately.

Here’s an important nugget of wisdom: being meticulous with your math can save you from making silly mistakes in a test setting. For instance, option B overcomplicates the original expression by adding a linear term that wasn't present. C plays with signs and ends up with a negative constant which doesn't match. D, while it has the right form, just miscalculates the constant.

So what? Why does this matter, right? Understanding the simplification and factoring not only helps with this question but sets a foundation for tackling more complex algebra concepts down the road. Plus, who doesn’t like feeling confident in their math skills?

In the grand scheme of things, practicing expressions like x² + 11x + 30 could be your key to acing that College Algebra CLEP Prep Exam. The more you get comfortable with factoring, the easier those tricky questions will seem when it’s exam day.

To wrap things up, remember the art of breaking things down. It’s kind of like baking a cake—you don’t throw all the ingredients in at once without knowing what each does, right? Similarly, braking down your algebra can help make the exam feel less like a mountain of stress and more like a friendly hike. Keep practicing, and soon, you’ll be cruising through algebra problems like a pro!