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Polynomials — 25-Question Test
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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 |
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