Calculation:

Consider the polynomial as,

\(5y^{3}+135\)

First, take 5 as common factor,

\(5y^{3}+135=5(y)^{3}+5(27)\)

\(=5(y^{3}+3^{3})\)

According to the factorized form of sum of two cubes, \(u^{3}+v^{3}=(u+v)(u^{2}—uv+v^{2})\).

\(5y^{3}+135=5(y+3)\left[y^{2}-y(3)+3^{2}\right]\)

\(=5(y+3)(y^{2}—3y+9)\)

Therefore, the factorization of the polynomial \(5y^{3}+135\) is \(5(y + 3)(y^{2}—3y+9)\).

Consider the polynomial as,

\(5y^{3}+135\)

First, take 5 as common factor,

\(5y^{3}+135=5(y)^{3}+5(27)\)

\(=5(y^{3}+3^{3})\)

According to the factorized form of sum of two cubes, \(u^{3}+v^{3}=(u+v)(u^{2}—uv+v^{2})\).

\(5y^{3}+135=5(y+3)\left[y^{2}-y(3)+3^{2}\right]\)

\(=5(y+3)(y^{2}—3y+9)\)

Therefore, the factorization of the polynomial \(5y^{3}+135\) is \(5(y + 3)(y^{2}—3y+9)\).