Find all real zeros of f(x)

Question

X⁴+2x³-3x²-8x-4

Answer 1

The only possible rational roots are 1,2,4 and -1, -2, and -4

If you plug in -1, you will find it is a root. Divide out the root by long division to get

x³ + x² - 4x - 4

Plug in -1 again and it is a root (i.e. a double root). Divide it out as before to get

x² - 4 which factors as (x + 2)(x - 2)

There you have it!