How would you use the remainder theorem for multiple factors?

[willow compass]

a) a=2 and b=4, but I don't really understand how to do b)

[mossy orbit]

Not sure how to do it with just remainder theorem tbh but if you know that any two polynomial a(x) and b(x) (at least when the coefficients are real numbers) can be written uniquely such that a(x) = b(x) q(x) + r(x), where r(x) has degree smaller than b(x) then the answer is right in front of you :p

So basically the division algorithm but with polynomials instead of integers

[willow compass]

thank you so much!!