Question

P(x) is a polynomial. here are a few values of p(x).

Answer 1

Given:

Values of a polynomial P(x).

$P(-5)=-2$

$P(-3)=6$

$P(3)=7$

$P(5)=-1$

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).

$P(-5)=-2$

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).

$P(3)=7$

Therefore, the remainder is 7 when P(x) is divided by (x-3).