# How to factor $y = x^5 + 20x^2 + 5$?

How would I factor to solve for x?

$x^5 + 20x^2 + 5=0$?

Do I use synthetic division? Is there a faster/easier way?

Do I have to keep plugging in numbers to see if they equal to zero?

Thanks! I'm not asking for full solutions if you don't want to share (but that would be nice) just opinions on what I should do.

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It could also be a quadratic times a cubic. – Will Jagy Oct 21 '13 at 0:42
Over the reals, this factors as a linear term and two quadratics -- none of them at all nice. – vadim123 Oct 21 '13 at 0:52
@StefanSmith, if you ask Wolfram Alpha kindly to factor it for you, it will give you numerical answers, showing one real root and four complex roots which appear to be conjugate pairs. – dfeuer Oct 21 '13 at 1:05
@dfeuer I'm sorry but I can't use Wolfram Alpha during tests. That would be nice though! So do you think you could show me exactly what you did? – Jessica Oct 21 '13 at 1:13
To sketch the function you don't need to factor the polynomial; just plug in a few points. – vadim123 Oct 21 '13 at 1:24