SATAdvanced (700+)Frequency: 1 question
Polynomial Remainder & Factor Theorem
When a polynomial P(x) is divided by (x - c), the remainder is simply P(c). If (x - c) is a factor of P(x), then the remainder is zero, meaning P(c) = 0.
Core Formula & Concept Cheat Sheet
1Remainder of P(x) / (x - c) is P(c)
2Factor theorem: (x - c) is a factor ⟺ P(c) = 0
The 700+ Score Trap
Plugging in -c instead of c (e.g. For dividing by x - 4, evaluate P(4), not P(-4)).
Test Your Mastery
Official Exam FormatLive Interactive Practice Drill
Let f(x) = 2x³ - 5x² + kx - 12. If (x - 3) is a factor of f(x), what is the value of k?
Frequently Asked Questions
Do I need to do long polynomial division on the Digital SAT?
Almost never! The Remainder Theorem allows you to find remainders in seconds just by evaluating P(c).