Answer :

We start with the polynomial

[tex]$$14x^3y^2 - 28x^3 + 56x^4.$$[/tex]

Step 1. Identify the Common Factor

Each term in the polynomial contains factors of [tex]$14$[/tex] and at least [tex]$x^3$[/tex]. We factor these out:

[tex]$$14x^3y^2 - 28x^3 + 56x^4 = 14x^3\left(y^2 - 2 + 4x\right).$$[/tex]

Step 2. Rearrange the Terms Inside the Parentheses

It is conventional to write the terms in a standard order (typically descending order in [tex]$x$[/tex]):

[tex]$$14x^3\left(y^2 - 2 + 4x\right) = 14x^3\left(4x + y^2 - 2\right).$$[/tex]

Thus, the completely factored form of the polynomial is

[tex]$$14x^3\left(4x + y^2 - 2\right).$$[/tex]

This is the final answer.