To factorize the quadratic expression \(-2x^2 - 14 - 24\), we first need to simplify the expression by combining like terms.

### Step 1: Combine like terms
The expression is already simplified as \(-2x^2 - 14 - 24\).

Combine the constants:
\[
-2x^2 - 38
\]

### Step 2: Factor out the greatest common factor (GCF)
The GCF of \(-2x^2\) and \(-38\) is \(-2\).

Factor out \(-2\):
\[
-2(x^2 + 19)
\]

Since \(x^2 + 19\) does not factor further (it's not a difference of squares or any other special factorization form), the fully factorized form of the expression is:
\[
\boxed{-2(x^2 + 19)}
\]

Would you like more details on this factorization or have any further questions?

Here are 5 related questions you might find interesting:
1. How do you factor a quadratic expression with three terms (e.g., \(ax^2 + bx + c\))?
2. What are the methods for solving quadratic equations?
3. How do you determine if a quadratic expression can be factored further?
4. What is the significance of the discriminant in quadratic equations?
5. How do you factor expressions involving higher-degree polynomials?

**Tip:** Always check if you can factor out a common factor before attempting other methods of factorization.

Learn how to factorize -2x^2 - 14 - 24 using step-by-step instructions and the greatest common factor (GCF) method. This problem involves algebraic manipulation and is suitable for advanced high school students (Grades 10-12).

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation