AI Tutor
If you can divide 756756 by 33 using long division, you already know almost everything you need to divide algebraic expressions.
A degree-three polynomial (or cubic) has x3x^3 as its highest power, while a degree-one divisor is a linear binomial like x−3x - 3.
Just like standard arithmetic, polynomial division runs on a four-step loop: Divide, Multiply, Subtract, and Bring down.
Let's see how this four-step loop works from start to finish on a complete cubic polynomial.

Step-by-Step Long Division

Let's divide 2x3−3x2−11x+62x^3 - 3x^2 - 11x + 6 by x−3x - 3.
First, divide the leading terms: 2x3x=2x2\frac{2x^3}{x} = 2x^2. Multiply 2x2(x−3)=2x3−6x22x^2(x - 3) = 2x^3 - 6x^2, subtract it to get 3x23x^2, and bring down −11x-11x.
Repeating the cycle with 3x2x=3x\frac{3x^2}{x} = 3x and −2xx=−2\frac{-2x}{x} = -2 gives a final quotient of 2x2+3x−22x^2 + 3x - 2 with a remainder of 00.
The most common mistake in polynomial long division is dropping signs during subtraction. When subtracting (2x3−6x2)(2x^3 - 6x^2), distribute the negative to make it −2x3+6x2-2x^3 + 6x^2 before combining.
What happens if our cubic polynomial skips a power of xx, like going straight from x3x^3 to xx?

Missing Terms and Remainders