For the given polynomial find all zeros of the polynomial al

For the given polynomial, find all zeros of the polynomial algebraically. Factor the polynomial completely.

P(x)= x^5 +3x^4 + 3x^3 -x^2 -4x-2

For the given polynomial, find all zeros of the polynomial algebraically. Factor the polynomial completely.

P(x)= x^5 +3x^4 + 3x^3 -x^2 -4x-2

For the given polynomial, find all zeros of the polynomial algebraically. Factor the polynomial completely.

using factor theorem, x =1 is zero

so dividing P(x) by x-1, we get = x^5 +3x^4 + 3x^3 -x^2 -4x-2 / x-1 = x^4+4x^3+7x^2+6x+2

again x = -1 is zero so x^4+4x^3+7x^2+6x+2/x+1 = x^3+3x^2+4x+2

again x =-1 is zero so x^3+3x^2+4x+2/x+1 = x^2+2x+2, which cannot be factorised and has complex roots

so solving it x= -1 +2i , -1-2i

so zeros are 1, -1, -1 +2i , -1-2i