Question 1190367
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Remainder Theorem:
If p(x) is divided over (x-k), then p(k) is the remainder.


Comparing x-3 to x-k shows that k = 3
p(x) = x^3-5x^2-14x+60
p(3) = 3^3-5(3)^2-14(3)+60
p(3) = 0
A remainder of zero confirms that x-3 is indeed a factor of x^3-5x^2-14x+60


Here's the polynomial long division
<img src = "https://i.imgur.com/EdjcLEZ.png">

And here's what the synthetic division looks like
<img src = "https://i.imgur.com/OeXSEvM.png">


Either way, you should find that
x^3-5x^2-14x+60 = (x-3)(x^2-2x-20)


You can use WolframAlpha or GeoGebra's CAS calculator to confirm. There are numerous other free calculators that will do the same type of thing.
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