2019 · Q59
What is (x - a)(x - b)(x - c) equal to?
Elementary MathematicsAlgebra
- Ax³ - (a + b + c)x² + (bc + ca + ab)x - abc
- Bx³ + (a + b + c)x² + (bc + ca + ab)x + abc
- Cx³ - (bc + ca + ab)x² + (a + b + c)x - abc
- Dx³ + (bc + ca + ab)x² - (a + b + c)x - abc
Explanation
Multiplying out: (x−a)(x−b) = x² − (a+b)x + ab, then × (x−c) gives x³ − (a+b+c)x² + (ab+bc+ca)x − abc. This is the standard cubic with roots a, b, c (Vieta's formulas); option (A) matches exactly, while the others flip signs.