AI Tutor
Think back to elementary school long division: divide, multiply, subtract, and bring down.
Believe it or not, dividing degree-three polynomials follows that exact same four-beat rhythm.
How do these familiar steps work when we are dealing with variables and exponents instead of single digits?

The Four-Step Cycle

A linear binomial is a two-term polynomial where the variable has an exponent of one, such as x−3x - 3.
In polynomial long division, we ignore the trailing terms at first and focus entirely on the leading terms to determine each step of the quotient.
Let's put this engine to work by dividing 2x3−3x2−11x+62x^3 - 3x^2 - 11x + 6 by x−3x - 3.
The single most common mistake in polynomial division happens during the subtraction phase.
When subtracting (2x3−6x2)(2x^3 - 6x^2), distribute the negative sign immediately to both terms to get −2x3+6x2-2x^3 + 6x^2, turning tricky subtraction into simple addition.
What happens when a polynomial skips an exponent or does not divide evenly?