How do you divide a polynomial by (x+1)

[laura_a]

Homework Statement

Let p(x)= (x+1)(x-3)Q(x) + a(x+1)+b

Where q(x) is a polynomial and a and b are real numbers

When p(x) is divided by (x+1) the remainder is 1, what is the value of b


I'm revising year 12 mathematics and I've forgotten how to divide polynomials
Is it

If I divided (x+1) by p(x) is it just = (x-3)q(x) + a + b so does that mean a+b is the remainder so a+b=1 therefore a = 1-b ?

Is that even close? :)

 

[mal4mac]

You seem to have divided OK for the first two terms, but doesn't b get divided by x + 1 as well?

As x varies then how can the remainder *always* be 1?