#1**+1 **

P(x) / (x-7) = x + 11/(x-7) (given) If you multiply both sides of this equation by (x-7) you will fid p(x)

p(x) = x (x-7) + 11

= x^2 - 7x + 11 then put 7 in for 'x' to find p(7) = 11

ElectricPavlov Feb 10, 2019

#2**+2 **

This is known as the "Remainder Theorem"

It says that if we divide some polynomial P(x) by x - a, then the remainder will be equal to P(a)

Cutting through the gobbledegook....let's look at an example

Suppose we divide x^2 - x - 6 by x - 3

We have that

x + 2

x - 3 [ x ^2 - x - 6 ]

x^2 - 3x

__________

2x - 6

2x - 6

______

0

Note that the remainder = 0

So....a = 3

And P(3) = (3)^2 - 3 - 6 = 0 ......the same as our remainder !!!!!

So..in your problem

a = 7

p(x) was divided by x - a and the remainder was 11

Which means that p(7) also = 11

CPhill Feb 10, 2019