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The given expression is:

\[
-42x^4 - 12x^2 + 30
\]

### Step 1: Look for the greatest common factor (GCF)
The GCF of the terms \( -42x^4 \), \( -12x^2 \), and \( 30 \) is 6. So, we can factor out 6 from the expression:

\[
6(-7x^4 - 2x^2 + 5)
\]

### Step 2: Factor the quadratic expression inside the parentheses
Now we are left with factoring the quadratic expression inside the parentheses:

\[
-7x^4 - 2x^2 + 5
\]

Let’s perform a substitution: let \( y = x^2 \), so the expression becomes:

\[
-7y^2 - 2y + 5
\]

We will attempt to factor this quadratic expression. Unfortunately, \( -7y^2 - 2y + 5 \) does not factor nicely over the integers, which means it's most likely irreducible in terms of integer factors.

### Final Answer:
The fully factored form is:

\[
6(-7x^4 - 2x^2 + 5)
\]

This is the simplest form for this expression.

Would you like more details on this process? 

Here are some related questions you might want to explore:
1. How do you find the greatest common factor (GCF) of an expression?
2. How do you factor quadratic equations?
3. What are irreducible quadratic expressions?
4. How can substitution be used to simplify higher-order polynomials?
5. How can you verify if a quadratic is factorable?

**Tip:** Always start by factoring out the greatest common factor (GCF) to simplify your expression.

Factor the expression -42x^4 - 12x^2 + 30. Simplify your answer as much as possible.

Learn how to factor the expression -42x^4 - 12x^2 + 30 using the greatest common factor (GCF) and substitution method. This step-by-step guide simplifies the expression and is suitable for students in Grades 9-11.

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