Question

Применить группировки
1) x^3-4x^2+12x-9
2) x^4+3x^3+4x^2+3x+1

Answer 1

(см. объяснение)

Объяснение:

Первое задание:

${x}^{3} - 4 {x}^{2} + 12x - 9 = {x}^{3} - {x}^{2} - 3 {x}^{2} + 3x + 9x - 9 = {x}^{2}(x - 1) - 3x(x - 1) + 9(x - 1) = (x - 1)( {x}^{2} - 3x + 9)$

Второе задание:

${x}^{4} + 3 {x}^{3} + 4 {x}^{2} + 3x + 1 = {x}^{4} + {x}^{3} + 2 {x}^{3} + 2 {x}^{2} + 2 {x}^{2} + 2x + x + 1 = {x}^{3} (x + 1) + 2 {x}^{2} (x + 1) + 2x(x + 1) + (x + 1) = (x + 1)( {x}^{3} + 2 {x}^{2} + 2x + 1) = (x + 1)( {x}^{3} + {x}^{2} + {x}^{2} + x + x + 1) = (x + 1)( {x}^{2} (x + 1) + x(x + 1) + (x + 1)) = {(x + 1)}^{2} ( {x}^{2} + x + 1)$