$-9m⁴+12m³+14m²-12m-5$. The question has been asked in iit genius exam of fitjee and is of class 8 level. We have to find all possible roots.
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1The usual first step is to look for rational roots. – lulu Feb 14 '20 at 12:34
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Hint: $m=1$ is a root. – Qurultay Feb 14 '20 at 12:34
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We only need to test for divisors of $9$ and $5$, see the answer below. – Dietrich Burde Feb 14 '20 at 12:41
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By the rational root theorem we find the rational roots $m=\pm 1,-\frac{1}{3},\frac{5}{3}$, so that $$ -9m^4+12m^3+14m^2-12m-5= - (3m + 1)(3m - 5)(m + 1)(m - 1). $$
Dietrich Burde
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