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Chapter 0: Problem 114

Factor completely. $$3 x^{2}+5 x y^{2}+2 y^{4}$$

Short Answer

Expert verified
The given polynomial \(3 x^{2}+5 x y^{2}+2 y^{4}\) is already factored completely.

Step by step solution

01

Identify the common factors

Inspect the given polynomial \(3 x^{2}+5 x y^{2}+2 y^{4}\) carefully and identify any common factors between all terms. In this case, there are no common factors across all terms.
02

Evaluate polynomial for group factorization

If there are no common factors across all terms, we need to evaluate if the polynomial can be factored by grouping. For this, we try to separate the terms into groups which contain a common factor. However, even by grouping there is no suitable way to factorize the polynomial further in this case.
03

Conclude

Since there are no common factors across all terms and we are unable to factorize the given polynomial by grouping, it can be concluded that \(3 x^{2}+5 x y^{2}+2 y^{4}\) is already factorized completely.

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