How do you factor x^3+2x^2+8x+4

Question

How do you do this using synthetic division?

Answer 1

I think you meant 2x³+x²+8x+4 because the given polynomial doesn't factor.

2x³+x²+8x+4=x²(2x+1)+4(2x+1)=(x²+4)(2x+1).

Synthetic division confirms that the real zero is x=-½.

-½ | 2  1 8    4

       2 -1 0 | -4

       2  0 8 |  0 = 2x²+8=2(x²+4).

2(x²+4)(x+½)=(x²+4)(2x+1).