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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