To find the factored form of the polynomial [tex]\( x^2 y^3 - 2 y^3 - 2 x^2 + 4 \)[/tex], let's break down the polynomial and look for common factors or group terms. Follow these steps:
1. Identify the polynomial:
[tex]\[ x^2 y^3 - 2 y^3 - 2 x^2 + 4 \][/tex]
2. Group the terms to look for common factors:
[tex]\[ (x^2 y^3 - 2 x^2) + (-2 y^3 + 4) \][/tex]
3. Factor out common terms within each group:
[tex]\[ x^2(y^3 - 2) - 2(y^3 - 2) \][/tex]
4. Notice that [tex]\( (y^3 - 2) \)[/tex] is a common factor in both groups:
[tex]\[ (y^3 - 2)(x^2 - 2) \][/tex]
So, the factored form of the polynomial [tex]\( x^2 y^3 - 2 y^3 - 2 x^2 + 4 \)[/tex] is:
[tex]\[ (x^2 - 2)(y^3 - 2) \][/tex]
To summarize, the polynomial [tex]\( x^2 y^3 - 2 y^3 - 2 x^2 + 4 \)[/tex] factors into [tex]\( (x^2 - 2)(y^3 - 2) \)[/tex].
