Question

The lcm of x^2-5x+6 and x^2-4x+3

Answer 1

Step-by-step explanation:

x3 + 8 = (x + 2)(x2 - 2x + 4)

x2 + 5x + 6 = (x + 2)(x + 3)

x3 + 4x2 + 4x = x(x2 + 4x + 4) = x(x + 2)2

LCM = x (x + 2)2 (x + 3) (x2 - 2x + 4)

Answer 2

Step-by-step explanation:

${x}^{2} - 5x + 6 \\ = {x}^{2} - 3x - 2x + 6 \\ = x(x - 3) - 2(x - 3) \\ (x - 3)(x - 2 \\ \\ {x}^{2} - 4x + 3 \\ = {x}^{2} - 3x - 1x + 3 \\ = x(x - 3) - 1(x - 3) \\ = (x - 3)(x - 1) \\ \\ \\ lcm \: is \: (x - 3)(x - 2)(x - 1) \\( {x}^{2} - 2x - 3x + 6)(x - 1) \\ {x}^{3} - {x}^{2} - 2 {?}^{2} + 2x - 3 {x}^{2} + 3x + 6x - 6 \\ {x}^{3} - 6 {x}^{2} + 11x - 11$

hope you get your answer