Posted by **Michelle** on Wednesday, December 21, 2011 at 11:11am.

solve the following equation in the complex number system Please show all your work.

5x^5 + 32x^4 - 5x - 32 = 0

- pre calculus -
**Steve**, Wednesday, December 21, 2011 at 11:42am
A little synthetic division shows

5x^5 + 32x^4 - 5x - 32

= (x-1)(x+1)(5x^3 + 32x^2 + 5x + 32)

Notice the 5,32 5,32 coefficients.

a little regrouping gives

(x-1)(x-1)(x^2(5x+32) + (5x+32))

(x-1)(x+1)(x^2 + 1)(5x+32)

Actually, we could have saved ourselves the synthetic division by noticing the 5,32,5,32 grouping at first:

(x^4 - 1)(5x+32)

You can probably take it from here . . .

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