Question

solve this equation using synthetic division x³+2x²+4x+8=0 list all the possible rational zeros for this polynomial and show work

Answer 1

First, let's see which value of x will make the polynomial to become zero

Let's check x= -2

x³+2x²+4x+8

substitute x = -2 into the above

(-2)³+2(-2)²+4(-2)+8

-8 + 8 - 8 + 8 = 0

x=-2 is one of the root

So, we will divide x³+2x²+4x+8 by x+2

The other factor is;

x² + 4

we can further simplify the above,

x² + 4 = 0

x² = -4

Take the square root of both-side

x =√ - 4

x = ± 2i

Hence the factors are

(x-2) (x + 2i ) (x- 2i)