Answer:
Step-by-step explanation:
To find the complete factored form of the polynomial \(44a^4 + 36b^6\), we start by looking for the greatest common factor (GCF) of the coefficients and the variables.
1. **Factor out the GCF:**
The GCF of \(44\) and \(36\) is \(4\). Also, the GCF of \(a^4\) and \(b^6\) is \(a^4\). Therefore, we can factor out \(4a^4\) from both terms:
\[
44a^4 + 36b^6 = 4a^4(11 + 9b^6)
\]
2. **Factor the remaining expression:**
Now, let's factor \(11 + 9b^6\). This expression cannot be factored further in terms of integers or simple binomials. Therefore, the complete factored form of the polynomial \(44a^4 + 36b^6\) is:
\[
\boxed{4a^4(11 + 9b^6)}
\]
This expression is fully factored over the integers and variables.
