Use the factor theorem to determine whether the binomial is a factor of the given polynomial.

Question

1. t+sqrt2; P(t)=t^5+t^4+4t+4
2. z-i; P(z)=z^7+z^6+z^5+z^4+z^3+z^2+z+1
3. z+2i; P(z)=z^3+z^2+4z+4

Thanks

Answer 1

1. P(-sqrt2)=-4sqrt2+4-4sqrt2+4 No
2. P(i)=-i-1+i+1-i-1+i+1=0 Yes
3. P(-2i)=8i-4-8i+4=0 Yes