Polynomial Long Division (quadratic)

The Polynomial Long Division (quadratic) computes Quotient from 4 inputs: a (ax²+bx+c), b, c, divide by (x − r). Divide a quadratic by a linear term.

Algebra is the art of solving for the unknown. Rearranging a formula to isolate the variable you actually need is the single most common real-world math skill — and doing it with real numbers under time pressure is where errors happen. The Polynomial Long Division (quadratic) sits in that toolkit — it divide a quadratic by a linear term. Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

Where

a

a (ax²+bx+c)

b

b

c

c

r

Divide by (x − r)

1. 01Start by noting the input — a (ax²+bx+c): 2.
2. 02Start by noting the input — b: 5.
3. 03Start by noting the input — c: -3.
4. 04Start by noting the input — Divide by (x − r): 1.
5. 05Substitute these values into the formula: {let t=e.a,a=e.b,n=e.c,r=e.r;return"".concat(t,"x + ").concat(t × r+a," (rem ").concat(n+(t × r+a) × r,")")}
6. 06Compute Quotient: the calculator returns 2x + 7 (rem 4).
7. 07Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.