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Synthetic Division: Computations w/ Radicals

• Given that  is a zero of x⁴ + 6x³ – 7x² – 30x + 10,
  fully solve the equation x⁴ + 6x³ – 7x² – 30x + 10 = 0.

You need to be very careful working problems like this. It's easy to make mistakes.

Do the first couple of steps:
Multiply to get the entry that goes under the –7:
Do the next couple of steps:
Multiply to get the entry that goes under the 10:
Complete the division:
Now you're ready for the next division, which works out like this:

Note that, since since this second synthetic division handled the conjugate radical root, all the complex coefficients disappeared. You should expect this to happen. Whenever you have roots that are conjugates, dividing out one of those roots will make things very messy, but then dividing out the other will clean things back up. Copyright © Elizabeth Stapel 1999-2009 All Rights Reserved

If you want to get the right answers, do not try to do the messier parts in your head or in the margins; take out a sheet of scratch paper and do your work properly.

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