Solve. Factor each expression. b.5y^{3}+135

Question
Polynomial factorization
asked 2021-01-08
Solve. Factor each expression.
b.\(5y^{3}+135\)

Answers (1)

2021-01-09
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 \(5(y + 3)(y^{2}—3y+9)\).
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