Question

Find remainder when x' + bx' + 4x - b is divided by x + b​

Answer 1

Answer:

First question

f(x)=x2+bx+a by remainder theorem and the condition given in the problem we have f(−2)=f(a), that means 4−2b+a=a2+ab+a which after factorized is equivalent to (a+2)(a+b−2)=0. Because a≠−2, a+b=2

Degree is the power of higest power term in polynomial. For example polynomial x100+8x37+1 has degree 100, constant has degree 0, etc.

By comparsion it's clear Q(x) has degree 1.

Plug in x=1 to the identity you get −9=a+b

Plug in x=−2 to the identity you get −24=−2a+b

Solve a,b you get a=5,b=−14