Answer :

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.