[tex] {x}^{2} + 3x + 2 = {x}^{2} + x + 2x + 2 = x(x + 1) + 2(x + 1) = (x + 1)(x + 2) \\ {x}^{2} + 5x + 4 = {x}^{2} + x + 4x + 4 = x(x + 1) + 4(x + 1) = (x + 1)(x + 4) \\ {x}^{2} + 7x + 12 = {x}^{2} + 3x + 4x + 12 = x(x + 3) + 4(x + 3) = (x + 3)(x + 4) \\ {x}^{2} + 5x + 6 = {x}^{2} + 2x + 3x + 6 = x(x + 2) + 3(x + 2) = (x + 2)(x + 3) \\ {x}^{2} + 7x + 10 = {x}^{2} + 2x + 5x + 10 = x(x + 2) + 5(x + 2) = (x + 2)(x + 5) \\ {x}^{2} + 9x + 20 = {x}^{2} + 4x + 5x = x(x + 4) + 5(x + 4) = (x + 4)(x + 5) \\ {x}^{2} + 8x + 15 = {x}^{2} + 3x + 5x + 15 = x(x + 3) + 5(x + 3) = (x + 3) +(x + 5) \\ {x}^{2} + 9x + 14 = {x}^{2} + 2x + 7x + 14 + 4 = x(x + 2) + 7(x + 2) = (x + 2)(x + 7) \\ {x}^{2} + 11x + 30 = {x}^{2} + 6x + 5x + 30 = x(x + 6) + 5(x + 6) = (x + 6)(x + 5) \\ {x}^{2} + 15x + 56 = {x}^{2} + 8x + 7x + 56 = x(x + 8) + 7(x + 8) = (x + 8)(x + 7) \\ {x}^{2} + 12x + 35 = {x}^{2} + 5x + 7x + 35 = x(x + 5) + 7(x + 5) = (x + 5)(x + 7) \\ {x}^{2} + 7x + 6 = {x}^{2} + x + 6x + 6 = x(x + 1) + 6(x + 1) = (x + 1)(x + 6) \\ {x}^{2} + 9x + 8 = {x}^{2} +x + 8x + 8 = x(x + 1) + 8(x + 1) = (x + 1)(x + 8) \\ {x}^{2} + 13x + 42 = {x}^{2} + 6x + 7x + 42 = x(x + 6) + 7(x + 6) = (x + 6) (x + 7) \\ {x}^{2} + 11x + 18 = {x}^{2} + 2x + 9x + 18 = x(x + 2) + 9(x + 2) = (x + 2)(x + 9)[/tex]
coroana?
