Question

Factor the polynomial completely

x^3+x^2+2x-4

Answer 1

Notice that 1 is a root of the polynomial. Hence x-1 divides x^3+x^2+2x-4.
Apply synthetic division:

1 | 1 1 2 -4
1 2 4
---------------
1 2 4 0

hence \(P(x)=(x-1)(x^2+2x+4)\)
\(=(x-1)( (x+1)^2+3)=(x-1)(x+1+\sqrt{3}i)(x+1-\sqrt{3}i)\)