Question

P(x) is a polynomial p(x) divided by (x-9) has a remainder of 1. P(x) divided by (x-4) has a remainder of 7. P(x) divided by (x+4) has a remainder of 0. P(x) divided by (x+9) has a remainder of -5
P(4)=?

P(-9)=?

Answer 1

Answer:

$P(4)=7\,,\,P(-9)=-5$

Step-by-step explanation:

Given:  P(x) has a remainder 1 when divided by  $x-9$, P(x) has a remainder 7 when divided by $x-4$, P(x) has a remainder 0 when divided by  $x+4$ and P(x) has a remainder -5 when divided by $x+9$

To find: $P(4),P(-9)$

Solution:

According to remainder theorem, when a polynomial $P(x)$ is divided by a polynomial $x-a$, the remainder obtained is equal to $P(a)$.

As P(x) has a remainder 7 when divided by $x-4$,

$P(4)=7$

As P(x) has a remainder -5 when divided by $x+9$,

$P(-9)=-5$