Synthetic Division Calculator With Fractions

Synthetic Division Method:

\[ \frac{a_nx^n + a_{n-1}x^{n-1} + \cdots + a_0}{x - c} = q(x) + \frac{r}{x - c} \]

Result:

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1. What is Synthetic Division?

Synthetic division is a shorthand method for dividing a polynomial by a linear divisor of the form (x - c). It's simpler and requires less writing than polynomial long division, especially when working with fractional coefficients.

2. How Synthetic Division Works

The synthetic division algorithm:

Write the coefficients of the polynomial
Bring down the leading coefficient
Multiply by the divisor and add to next coefficient
Repeat until all coefficients are processed
The last number is the remainder

3. Handling Fractional Coefficients

Details: This calculator properly handles fractional coefficients by converting them to decimal values during computation. The process remains identical to integer coefficients.

4. Using the Calculator

Tips: Enter coefficients as fractions (e.g., "1/2, -3/4, 5/8") from highest to lowest degree. Enter the divisor c from (x - c) as a fraction.

5. Frequently Asked Questions (FAQ)

Q1: Can I use mixed numbers?
A: No, enter fractions as improper fractions (e.g., 3/2 instead of 1 1/2).

Q2: What if my polynomial has missing terms?
A: Include 0 coefficients for missing degrees (e.g., x³+1 becomes "1, 0, 0, 1").

Q3: How accurate are the results with fractions?
A: The calculator maintains floating point precision throughout the computation.

Q4: Can I divide by quadratic polynomials?
A: No, synthetic division only works for linear divisors of form (x - c).

Q5: What does the remainder represent?
A: The remainder is the value of the polynomial evaluated at x = c.