Polynomial relationship problem

[Michael_Light]

Homework Statement

Polynomials p(x) and q(x) are given by relationship q(x)=p(x)(x⁵-2x+2).

a) If x-2 is a factor of p(x)-5 , find the remainder when q(x) is divided by x-2.

b) If p(x) is of the form x²+ax+b and x-1 is a factor of p(x)-5, find the values of a and b.

Homework Equations

The Attempt at a Solution

Can anyone help?

 

[Mentallic]

For -

a) use the idea that if a polynomial p(x) has a root at a=0, then p(a)=0

b) Using the same idea as above, you should be able to establish an equation with the two unknowns a and b in it. To find another equation so that you can solve them simultaneously, use your answer from a).