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Factor $y^6-23y^3-50\text{.}$

Solution

We need a pair of numbers that multiply to $-50$ and add to $-23\text{.}$ Note that we do care to keep track that they multiply to a negative product and sum to a negative total.

Factor Pair	Sum of the Pair
$1\cdot(-50)$	$-49$
$2\cdot(-25)$	$-23$ (what we wanted)
(no need to continue)	...

So $y^6-23y^3-50=\left(y^3-25\right)\left(y^3+2\right)\text{.}$