Rewrite rational expressions

What you'll learn

1. Rewrite a rational expression a(x)/b(x) in the form q(x) + r(x)/b(x) by performing polynomial long division
2. Identify when a rational expression is a proper fraction (degree of numerator < degree of denominator) vs. an improper fraction, and explain why the division algorithm is needed for improper cases
3. Perform polynomial long division step by step, correctly handling missing degree terms
4. Verify the result of polynomial division using the check: a(x) = b(x)·q(x) + r(x)
5. Recognize when the remainder is zero, interpreting this in terms of the Factor Theorem (b(x) divides a(x) evenly)

Prerequisites

• Perform polynomial operations
• Apply the Remainder Theorem