Problem 2

Divide by

Solution
a) Rewrite in standard form. The numerator becomes

and the denominator becomes

b) Factor the denominator by pulling out a negative sign:

Thus, the division is equivalent to

c)Set up the division. We expect a quadratic quotient such that

d) Multiply out and equate coefficients. The product expands to

Equate this with

For : so

For : yields so

For : gives so and

For the term: with and this checks.

The constant term gives which matches.

Answer: