Polynomial Long Division Calculator
Algebra, Polynomials
Intro: Performs polynomial long division to find quotient q(x) and remainder r(x), mirroring the step-by-step layout used in class.
Worked example
- Compute $(x^3 - 2x^2 + 4x - 8) ÷ (x - 2)$ using long division.
- We divide $f(x)=x^3-2x^2+4x-8$ by $g(x)=x-2$ using polynomial long division.
- Step 1: Divide leading terms: $x^3 / x = x^2$. This is the first term of the quotient $q(x)$.
- Multiply the divisor by this term: $(x-2)\cdot x^2 = x^3 - 2x^2$.
- Subtract this from the original polynomial: $(x^3-2x^2+4x-8) - (x^3-2x^2) = 4x-8$.
- Bring down the remaining terms (here $4x-8$ is already what remains).
- Step 2: Divide new leading term: $4x/x = 4$. Add $+4$ to the quotient, so $q(x) = x^2 + 4$.
- Multiply divisor by 4: $(x-2)\cdot4 = 4x - 8$.
- Subtract: $(4x-8)-(4x-8)=0$, so the remainder is $r(x)=0$.
- Thus $x^3-2x^2+4x-8 = (x-2)(x^2+4) + 0$.
- Answer: $\boxed{q(x)=x^2+4,\; r(x)=0}$.
FAQs
Can this handle missing terms like x²?
Yes. We internally rewrite polynomials with zero coefficients so long division works correctly.
Why choose MathGPT?
- Get clear, step-by-step solutions that explain the “why,” not just the answer.
- See the rules used at each step (power, product, quotient, chain, and more).
- Optional animated walk-throughs to make tricky ideas click faster.
- Clean LaTeX rendering for notes, homework, and study guides.
How this calculator works
- Type or paste your function (LaTeX like
\sin,\lnworks too). - Press Generate a practice question button to generate the derivative and the full reasoning.
- Review each step to understand which rule was applied and why.
- Practice with similar problems to lock in the method.