Given:
Values of a polynomial P(x).
![P(-5)=-2](/tpl/images/1389/7459/a1279.png)
![P(-3)=6](/tpl/images/1389/7459/86103.png)
![P(3)=7](/tpl/images/1389/7459/95234.png)
![P(5)=-1](/tpl/images/1389/7459/506bc.png)
To find:
The remainder when P(x) is divided by (x+5).
The remainder when P(x) is divided by (x-3).
Solution:
If a polynomial P(x) is divided by (x-a), then the remainder is P(a).
If the polynomial P(x) is divided by (x+5), then the remainder is P(-5).
![P(-5)=-2](/tpl/images/1389/7459/a1279.png)
Therefore, the remainder is -2 when P(x) is divided by (x+5).
If the polynomial P(x) is divided by (x-3), then the remainder is P(3).
![P(3)=7](/tpl/images/1389/7459/95234.png)
Therefore, the remainder is 7 when P(x) is divided by (x-3).