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.
[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.
