Problem 114
Question
Factor completely. $$3 x^{2}+5 x y^{2}+2 y^{4}$$
Step-by-Step Solution
Verified Answer
The given polynomial \(3 x^{2}+5 x y^{2}+2 y^{4}\) is already factored completely.
1Step 1: 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.
2Step 2: 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.
3Step 3: 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.
Other exercises in this chapter
Problem 113
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Simplify each exponential expression. Assume that variables represent nonzero real numbers. $$ \frac{\left(2^{-1} x^{-3} y^{-1}\right)^{-2}\left(2 x^{-6} y^{4}\
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