aspifsGak5u

2021-12-15

Factor the polynomial. $15{x}^{3}{y}^{5}-25{x}^{4}{y}^{2}+10{x}^{6}{y}^{4}$

Expert

Given
The polynomial is
$\left(15×3\right){y}^{5}-\left(25×4\right){y}^{2}+\left(10×6\right){y}^{4}$
Simplify
The polynomial is
$\left(15×3\right){y}^{5}-\left(25×4\right){y}^{2}+\left(10×6\right){y}^{4}$
$=45{y}^{5}+60{y}^{4}-100{y}^{2}$
$={y}^{2}\left(45{y}^{3}+60{y}^{2}-100\right)$
$\left(15×3\right){y}^{5}-\left(25×4\right){y}^{2}+\left(10×6\right){y}^{4}={y}^{2}\left(15{y}^{2}\left(3y+4\right)-100\right)$

Maria Lopez

Expert

As the co-efficient of the given polynomials are integers, therefore factoring out
The gcf $5{x}^{3}{y}^{2}$, we can write,
$15{x}^{3}{y}^{5}-25{x}^{4}{y}^{2}+10{x}^{6}{y}^{4}=5{x}^{3}{y}^{2}\left(3{y}^{3}-5x+2{x}^{3}{y}^{2}\right)$
Hence, the required factor is $5{x}^{3}{y}^{2}\left(3{y}^{3}-5x+2{x}^{3}{y}^{2}\right)$

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The text contains a mathematical question asking to factor a polynomial, and it provides two different answers to the question.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
aspifsGak5u

2021-12-15

Factor the polynomial. $15{x}^{3}{y}^{5}-25{x}^{4}{y}^{2}+10{x}^{6}{y}^{4}$

Expert

Given
The polynomial is
$\left(15×3\right){y}^{5}-\left(25×4\right){y}^{2}+\left(10×6\right){y}^{4}$
Simplify
The polynomial is
$\left(15×3\right){y}^{5}-\left(25×4\right){y}^{2}+\left(10×6\right){y}^{4}$
$=45{y}^{5}+60{y}^{4}-100{y}^{2}$
$={y}^{2}\left(45{y}^{3}+60{y}^{2}-100\right)$
$\left(15×3\right){y}^{5}-\left(25×4\right){y}^{2}+\left(10×6\right){y}^{4}={y}^{2}\left(15{y}^{2}\left(3y+4\right)-100\right)$

Maria Lopez

Expert

As the co-efficient of the given polynomials are integers, therefore factoring out
The gcf $5{x}^{3}{y}^{2}$, we can write,
$15{x}^{3}{y}^{5}-25{x}^{4}{y}^{2}+10{x}^{6}{y}^{4}=5{x}^{3}{y}^{2}\left(3{y}^{3}-5x+2{x}^{3}{y}^{2}\right)$
Hence, the required factor is $5{x}^{3}{y}^{2}\left(3{y}^{3}-5x+2{x}^{3}{y}^{2}\right)$

Do you have a similar question?
user
The text contains a mathematical question asking to factor a polynomial, and it provides two different answers to the question.

TYPE: SINGLE_QUESTION_WITH_ANSWER