Synthetic Division
Our Synthetic Division Calculator helps you quickly divide polynomials by a linear factor (x - k). Just enter the coefficients of your polynomial and the root 'k' from your divisor, and we'll show you the quotient and remainder.
Enter coefficients separated by spaces, from highest degree to constant term. Use 0 for missing terms (e.g., '1 0 -7 6' for x³ - 7x + 6).
If your divisor is (x - k), enter 'k'. If it's (x + k), enter '-k'.
Our Synthetic Division Calculator helps you quickly divide polynomials by a linear factor (x - k). Just enter the coefficients of your polynomial and the root 'k' from your divisor, and we'll show you the quotient and remainder.
For a polynomial P(x) and a linear divisor (x - k), synthetic division finds the quotient Q(x) and remainder R such that P(x) = Q(x)(x - k) + R.
To divide x³ - 7x + 6 by x - 2, enter the coefficients '1 0 -7 6' (note the 0 for the missing x² term) and the root '2' (since x - 2 = 0 implies x = 2). The calculator will output a quotient of x² + 2x - 3 and a remainder of 0.
Synthetic division is a shortcut method for dividing polynomials by linear factors of the form (x - k). It's particularly useful for finding roots of polynomials, factoring polynomials, and evaluating polynomial functions.
When setting up synthetic division, you must include a zero for any missing powers of x. For example, if you have x³ + 5, you'd represent its coefficients as 1 (for x³), 0 (for x²), 0 (for x¹), and 5 (for the constant term).
If your divisor is (x + k), you should rewrite it as (x - (-k)). This means you'll use -k as your divisor root in the synthetic division process. For example, for (x + 3), use -3 as the root.
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