Synthetic division: a quick method
Synthetic division is a shortcut for dividing a polynomial by a linear factor of the form (x-c). It works best when the polynomial is written in descending powers of (x).
Steps to follow
- Write the coefficients of the dividend in order. If a power is missing, use 0 for that term.
- Use the number (c) from (x-c). For example, divide by (x-3) means use (3); divide by (x+2) means use (-2).
- Bring down the first coefficient.
- Multiply and add repeatedly: multiply the number you just brought down by (c), write the result under the next coefficient, then add. Continue across the row.
- The final row gives the quotient coefficients. The last number is the remainder.
How to write the answer
If the remainder is 0, the division is exact. Otherwise, write the quotient plus the remainder over the divisor.
Check your work
You can check your result by multiplying the quotient by (x-c) and adding the remainder. The result should match the original polynomial.
Common mistakes
- Skipping a missing term instead of using 0
- Using the wrong sign for (c)
- Forgetting that the last number is a remainder, not part of the quotient