Divide a polynomial by x − c using a compact coefficient recurrence. Its quotient and remainder sits beside the working formula for a quick arithmetic check.
Preserve Dividend coefficients, highest power first when checking the Synthetic Division output. Keep Value c in divisor x − c under the same convention and estimate Quotient and remainder. A controlled change to Value c in divisor x − c should move the Synthetic Division Quotient and remainder in a mathematically consistent direction.
Bring down the first coefficient. Multiply it by c, add to the next coefficient, and repeat through the constant term.
It quickly evaluates factors, tests proposed roots, and divides by monic linear expressions without writing every power of x.
The divisor must have form x−c with leading coefficient one. Preserve zero coefficients for missing powers.
Synthetic division brings down the leading coefficient, then repeatedly multiplies by c and adds the next coefficient. The final entry is the remainder. Synthetic Division also connects with general polynomial division.
Polynomial long division handles broader divisors; synthetic division is a shortcut for one monic linear divisor. Here the requested quantity is specifically quotient and remainder.
Dividing x³−6x²+11x−6 by x−2 gives quotient x²−4x+3 and remainder zero. This Synthetic Division example can be compared with check P(c).
Substitute the Synthetic Division solution into Dividend coefficients, highest power first. This Synthetic Division check rejects false Synthetic Division branches and forbidden denominators.
Choose an easy Dividend coefficients, highest power first value before running Synthetic Division. Predict Value c in divisor x − c, then compare it with the Synthetic Division output.
Reverse the Synthetic Division reasoning once: begin with the shown Quotient and remainder and ask whether Dividend coefficients, highest power first could produce it under Value c in divisor x − c. When that Synthetic Division relationship fails, the contradiction narrows the error to an entry, order choice, or convention.
x−c is a factor.
They preserve missing powers.
Yes; enter c=−3.
One less than the dividend degree.