Разложите многочлен ** множители 3х³-6х²-15х+18=0

Question

Разложите многочлен на множители 3х³-6х²-15х+18=0

Answer 1

3х^3 – 6х^2 – 15х + 18 = 0
3(х^3 – 2х^2 – 5х + 6) = 0
3(х^3 – х^2 – х^2 + х – 6х + 6) = 0
3(х^2 • (х – 1) – х • (х – 1) – 6(х – 1)) = 0
3(х – 1) • (х^2 – х – 6) = 0
3(х – 1) • (х^2 + 2х – 3х – 6) = 0
3(х – 1) • (х • (х + 2) – 3(х + 2)) = 0
3(х – 1) • (х – 3) • (х + 2) = 0
(х – 1) • (х – 3) • (х + 2) = 0
х – 1 = 0
х – 3 = 0
х + 2 = 0
х = 1
х = 3
х = – 2