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

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

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`