## anonymous 5 years ago Factor the polynomial completely x^3+x^2+2x-4

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