Final answer:
To factor 12d-72e, first find the GCF, which is 12. The factored form of the expression is 12(d - 6e), where d and -6e are the terms of the missing factor.
Step-by-step explanation:
To factor the expression 12d-72e using the area model, you must first find the greatest common factor (GCF) that both terms share. Here, both 12 and 72 are divisible by 12, and the variable d is only in the first term, so it's not part of the GCF. The GCF of these two terms is 12. Once you have the GCF, you can factor it out from both terms.
The remaining terms become d and -6e, as to get back to the original terms, we would multiply them by 12 (our GCF).
Now, writing the expression in factored form, we have 12(d - 6e). This shows the two factors of the original expression: 12 and (d - 6e).