Question

Show that -1, -5 & -6 are the zeroes of y^3 + 12y^2 + 41y + 30

Answer 1

${y}^{3} + 12 {y}^{2} + 41y + 30 \\ {y}^{3} + {y}^{2} + 11 {y}^{2} + 11y + 30y + 30 \\ {y}^{2} (y + 1) + 11y(y + 1) + 30(y + 1) \\ (y + 1)( {y}^{2} + 11y + 30) \\ (y + 1)( {y}^{2} + 6y + 5y + 30) \\ (y + 1)(y(y + 6) + 5(y + 6)) \\ (y + 1)(y + 5)(y + 6)$