Synthetic Division Calculator
Algebra, Polynomials
Intro: Applies synthetic division to divide a polynomial by x − c, giving the quotient coefficients and remainder (which equals f(c)).
Worked example
- Use synthetic division to divide $f(x)=2x^3−3x^2+4x−5$ by $x−2$.
- We divide $f(x)=2x^3-3x^2+4x-5$ by $x-2$ using synthetic division with $c=2$.
- Write the coefficients of f(x): $2, -3, 4, -5$.
- Bring down the leading coefficient: write 2 in the bottom row.
- Multiply by c: $2\cdot2=4$, and write 4 under the next coefficient -3, then add: $-3+4=1$.
- Multiply the new number by c: $1\cdot2=2$, place under the next coefficient 4, then add: $4+2=6$.
- Multiply again: $6\cdot2=12$, place under the last coefficient -5, then add: $-5+12=7$.
- The bottom row now reads $2, 1, 6, 7$. The first three numbers are coefficients of the quotient, and the last number is the remainder.
- Since we started with degree 3, the quotient is $2x^2 + 1x + 6$, and the remainder is $7$.
- So $f(x)=(x-2)(2x^2+x+6)+7$.
- Answer: $\boxed{q(x)=2x^2+x+6,\; r=7,\; f(2)=7.}$
FAQs
Can I divide by x + c?
Yes. Dividing by x + c is the same as synthetic division with c = −c (i.e., use the root x = −c).
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.