Divide one polynomial by another and report quotient and remainder coefficient lists. The result panel keeps polynomial quotient and its numerical trail together.
Polynomial long division cancels the current leading term by multiplying the divisor by a suitable monomial, subtracting, and repeating.
Divide leading terms, append that quotient term, subtract the shifted divisor multiple, and continue until the remainder degree is smaller. To continue from Polynomial Long Division, try linear shortcut.
Dividing [1,−6,11,−6] by [1,−2] yields quotient [1,−4,3] and remainder [0].
It supports rational expressions, factorization, asymptotes, and algebraic simplification when the divisor has any nonzero leading coefficient. A related application of Polynomial Long Division is reconstruct the dividend.
The zero polynomial cannot be a divisor. Coefficient lists must keep internal zeros and run from highest power to constant.
The relationship between Dividend coefficients, highest power first and Polynomial quotient provides another check on Polynomial Long Division. Move Dividend coefficients, highest power first slightly while keeping Divisor coefficients, highest power first constant, then decide in advance whether Polynomial quotient ought to rise, fall, or remain unchanged.
Rework Polynomial Long Division without copying Polynomial quotient. Begin with Dividend coefficients, highest power first and preserve Divisor coefficients, highest power first. Predict the scale of the Polynomial Long Division answer, then compare it with Polynomial quotient. Store a changed Divisor coefficients, highest power first as another Polynomial Long Division case.
Challenge Polynomial quotient with a nearby value of Dividend coefficients, highest power first. Leave Divisor coefficients, highest power first fixed during the Polynomial Long Division trial. The direction of the new Polynomial quotient should agree with the underlying Polynomial Long Division relationship.
Change only Dividend coefficients, highest power first during a Polynomial Long Division trial. With Divisor coefficients, highest power first unchanged, the movement in Polynomial quotient should follow the stated mathematical relationship.
Record the first Polynomial Long Division setup before editing Dividend coefficients, highest power first. A later value of Polynomial quotient should remain attached to its own inputs.
Multiply divisor by quotient and add remainder.
No.
They do not change the polynomial degree.
Yes.