Module 3 · Advanced Algebra
Chapter 12: Polynomials
Advanced Math
4 topics
What this chapter covers
The 4 topics below make up Polynomials on the Digital SAT. Click any topic to open its notes, examples and practice test.
Study material & tests
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Notes, worked examples and hint-guided practice for every topic.
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🎯 Topic tests
8 auto-graded questions per topic, pulled from the question bank.
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📝 Chapter test
25 fresh mixed-difficulty questions, timed, with full solutions.
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Formula Reference Sheet
This chapter
Terminology
| Degree | highest exponent in the polynomial |
|---|---|
| Leading coefficient | coefficient of the highest-degree term |
| Monomial / binomial / trinomial | 1 / 2 / 3 terms |
Key products & factors
| FOIL | (a + b)(c + d) = ac + ad + bc + bd |
|---|---|
| Difference of squares | a² − b² = (a + b)(a − b) |
| Perfect square | a² ± 2ab + b² = (a ± b)² |
| Common factor | factor out the GCF first |
Digital SAT reference
Area & Circumference
| Circle area | A = πr² |
|---|---|
| Circle circumference | C = 2πr |
| Rectangle | A = ℓw |
| Triangle | A = ½ b h |
Volume
| Rectangular box | V = ℓwh |
|---|---|
| Cylinder | V = πr²h |
| Sphere | V = 4⁄3 πr³ |
| Cone | V = 1⁄3 πr²h |
| Pyramid | V = 1⁄3 ℓwh |
Right triangles
| Pythagorean theorem | a² + b² = c² |
|---|---|
| 30°–60°–90° | sides x : x√3 : 2x |
| 45°–45°–90° | sides s : s : s√2 |
Constants
| Degrees in a circle | 360° |
|---|---|
| Radians in a circle | 2π |
| Angles of a triangle | sum = 180° |
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