Factor the expression completely.
minus, 24, x, to the power 4 , minus, 42, x, cubed
−24x
4
−42x
3

We are given the expression:

\[
-24x^4 - 42x^3
\]

### Step 1: Factor out the greatest common factor (GCF)
The GCF of \(-24x^4\) and \(-42x^3\) is \(-6x^3\). Let's factor it out:

\[
-6x^3(4x + 7)
\]

### Final Answer:
The fully factored form of the expression is:

\[
-6x^3(4x + 7)
\]

Would you like further details or clarification on this? Here are some related questions you might find useful:

1. How do you determine the greatest common factor of terms in an expression?
2. How can you check if your factored expression is correct?
3. What are the rules for factoring polynomials with multiple terms?
4. What is the significance of factoring in solving equations?
5. How do you factor expressions with higher-degree terms?

**Tip**: Always check your factorization by multiplying the factors back together to ensure you recover the original expression.

Factor the expression completely: −24x^4 − 42x^3.

Learn how to factor the polynomial expression −24x^4 − 42x^3 completely by finding the greatest common factor (GCF) and applying the distributive property. This solution covers key algebraic concepts, including factoring and polynomial manipulation. Suitable for students in Grades 8-10.

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