Question

Разложите на линейные множители выражение 2x³+5x²-4x-3

Answer 1

$2 {x}^{3} + 5 {x}^{2} - 4x - 3 = 2 {x}^{3} - 2 {x}^{2} + 7 {x}^{2} - 7x + 3x - 3 = 2 {x}^{2} (x - 1) + 7x( x- 1) + 3(x - 1) = (x - 1)(2 {x}^{2} + 7x + 3) = (x - 1)(2 {x}^{2} + 6x + x + 3) = (x - 1)(2x(x + 3) + x + 3) = (x - 1)(x + 3)(2x + 1)$