How do you factor $10 m^{3} n^{2} - 15 m^{2} n + 25 m$ $10m^3n^2-15m^2n+25m$ ?

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How do you factor $10 m^{3} n^{2} - 15 m^{2} n + 25 m$ $10m^3n^2-15m^2n+25m$ ?

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Answer 1 · 2015-05-10T22:06:27

$10 m^{3} n^{2} - 15 m^{2} n + 25 m = 5 m (2 m^{2} n^{2} - 3 m n + 5)$ $10m^3n^2-15m^2n+25m = 5m(2m^2n^2-3mn+5)$

To see that this does not factor further, let $p = m n$ $p=mn$ .

Then $2 m^{2} n^{2} - 3 m n + 5 = 2 p^{2} - 3 p + 5$ $2m^2n^2-3mn+5=2p^2-3p+5$

If this had linear factors, then it would factorise as $(2 p - 1) (p - 5)$ $(2p-1)(p-5)$ or $(2 p - 5) (p - 1)$ $(2p-5)(p-1)$ in order to get the coefficient of $p^{2}$ $p^2$ and the constant term correct. Neither of these works.

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How do you factor $10 m^{3} n^{2} - 15 m^{2} n + 25 m$ $10m^3n^2-15m^2n+25m$ ?

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How do you factor $10 m^{3} n^{2} - 15 m^{2} n + 25 m$ $10m^3n^2-15m^2n+25m$ ?