Module 2 · Algebra
Chapter 18: Polynomials
Algebra
4 topics
🎯 1 practice questions
What this chapter covers
The 4 topics below make up Polynomials on the CAT. 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
Algebraic identities
| Square of a sum/difference | (a ± b)² = a² ± 2ab + b² |
|---|---|
| Difference of squares | a² − b² = (a − b)(a + b) |
| Cube of a sum/difference | (a ± b)³ = a³ ± 3a²b + 3ab² ± b³ |
| Sum/difference of cubes | a³ ± b³ = (a ± b)(a² ∓ ab + b²) |
| Three-cube identity | a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c² − ab − bc − ca) |
| Square of a trinomial | (a + b + c)² = a² + b² + c² + 2(ab + bc + ca) |
Division & roots tools
| Remainder theorem | Remainder of P(x) ÷ (x − a) is P(a) |
|---|---|
| Factor theorem | (x − a) divides P(x) ⇔ P(a) = 0 |
| Vieta — quadratic ax²+bx+c | sum = −b/a, product = c/a |
| Vieta — cubic ax³+bx²+cx+d | Σα = −b/a, Σαβ = c/a, αβγ = −d/a |
| Sum of squares of roots | Σα² = (Σα)² − 2Σαβ |
| When a+b+c = 0 | a³ + b³ + c³ = 3abc |
CAT reference
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