pre calculus
posted by Michelle .
solve the following equation in the complex number system Please show all your work.
5x^5 + 32x^4  5x  32 = 0

A little synthetic division shows
5x^5 + 32x^4  5x  32
= (x1)(x+1)(5x^3 + 32x^2 + 5x + 32)
Notice the 5,32 5,32 coefficients.
a little regrouping gives
(x1)(x1)(x^2(5x+32) + (5x+32))
(x1)(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 . . .