Polynomial Long Division With a Missing Term (Updated), by Brian McLogan on YouTube. 8 min 21 s.
- Video length
- 8 min 21 s
- Time to do it
- 20 minutes
- Difficulty
- Medium
- Steps
- 8
What you need
Steps
Write the dividend and divisor in descending order of their exponents. Check which powers of x are missing from the dividend, since those gaps cause most mistakes.
Fill each missing power with a zero term, such as 0x squared or 0x. This keeps every column lined up during the division.
Divide the first term of the dividend by the first term of the divisor. Write the result above the matching column as the first part of your quotient.
Multiply that quotient term by the whole divisor. Write the product under the dividend, lining up like terms in the same columns.
Subtract the product from the dividend, putting parentheses around the product so every sign flips correctly. Bring down the next term to form a new working polynomial.
Repeat the divide, multiply and subtract cycle with the new polynomial. Keep going until the remaining polynomial has a lower degree than the divisor.
Collect all the quotient terms you wrote on top into one expression. The leftover polynomial becomes the remainder.
Write the final answer as the quotient plus the remainder over the divisor. Check by multiplying the quotient by the divisor and adding the remainder.
Tips and common mistakes
Always include the zero terms for missing powers, or your columns will shift and the answer will be wrong.
Use parentheses on every subtraction line, since dropping a minus sign is the most common error.
Line up like terms in vertical columns so each exponent stays in its own place.
Check your result by multiplying the quotient by the divisor and adding the remainder to see if you get the dividend back.
Questions
What does a missing term mean in polynomial long division?
It means the dividend skips a power of x, like going from x cubed straight to x. You add a zero coefficient for that power so the columns stay aligned.
How do I know when to stop dividing?
Stop when the remaining polynomial has a lower degree than the divisor. Whatever is left becomes the remainder.
Do I have to write the remainder as a fraction?
Yes, unless the remainder is zero. Write it as the remainder divided by the original divisor, added to the quotient.
This guide was drafted from the video's details and general task knowledge. It has not been checked against the full video. Check the video and relevant product instructions before following a procedure. Report a correction.
