Answer:
The two polynomials cannot be factored using integer coefficients. Therefore, we need to use the quadratic formula to find their roots:
For x² - 3x + 2 = 0:
a = 1, b = -3, c = 2
x = (-(-3) ± √((-3)² - 4(1)(2))) / (2(1)) = (3 ± √1) / 2
x = 1 or x = 2
For x² + x + 2 = 0:
a = 1, b = 1, c = 2
x = (-1 ± √(1² - 4(1)(2))) / (2(1)) = (-1 ± √(-7)) / 2
x = (-1 ± i√7) / 2
Therefore, the LCM of x² - 3x + 2 and x² + x + 2 is:
(x - 1)(x - 2)(x - (-1/2 + i√7/2))(x - (-1/2 - i√7/2))