Answers:
First statements: True
![(-5)^4+5(-5)^3+(-5)^2-5(-5)=0](https://img.qammunity.org/2019/formulas/mathematics/high-school/atkmvqid5l5d0tcb5ddqy48hcbnoo39jh2.png)
Second statement: False
![(x^4+5x^3+-x^2-5x)/(x+5) = x (x - 1) (x + 1)](https://img.qammunity.org/2019/formulas/mathematics/high-school/rkbzvzlhbx505g4x8sgh5ocuxotx4uw5n4.png)
Third statement: False
5 is not a root of this polynomial, therefore (x-5) is not one of its factors/
Fourth statement: False
5 is not a root of this polynomial, therefore f(5) does not equal 0.