SAT Math: Polynomial Long Division and Synthetic Routes
21+ practice questions in Praczo
The concept, explained
- 1
When simplifying a rational expression like (x² + 5x + 6) / (x + 2), you can often factor the top and cancel the bottom.
- 2
If it doesn't factor cleanly, or if the degree of the numerator is higher, polynomial long division can produce a quotient and a remainder.
- 3
The result is written as: Quotient + (Remainder / Divisor).
- 4
Synthetic division is a faster shortcut but only works when dividing by a linear binomial (x - c).
- 5
The Remainder Theorem: The remainder when dividing a polynomial P(x) by (x - c) is exactly equal to P(c).
- ✗ Forgetting to write the remainder over the original divisor in the final expression.
- ✗ When doing synthetic division, forgetting to use the zero of the divisor (e.g., using -2 instead of 2 for x + 2).
SAT-style practice
If (x² + 3x + 5) is divided by (x + 1), what is the remainder?
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