Question

if the zeros of a polynomial x 4 + 2 x cube minus x square - 2x are zeros, 1 and -1 them all the zeros​

Answer 1

Step-by-step explanation:

Let

p(x)=x^4+2x^3-x^2-2x

we have two zeroes for p(x), 1 & -1. Checking them one by one using factor theorem,

Firstly, putting x=1 in p(x)

p(1)= (1)^4 + 2(1)^3 - (1)^2 - 2(1)

p(1)= 1 + 2 + 1 - 2

p(1)= 3 - 3

p(1)= 0

checked

In the same way, when we put x=-1, then the answer is 0.

Therefore, x+1 and x-1 both are the factors of p(x).