ЯсноПонятно24

To find the solutions for x, we need to set each factor equal to zero and solve for x.

Setting x + 1 = 0, we get: x = -1

Setting 2x³ - 5x² - 8x + 13 = 0, we can factor this cubic polynomial to find its roots. By trying different values of x, we find that x = 1 is a root. Therefore, we can divide the polynomial by (x-1) to get the quadratic factor:

(2x³ - 5x² - 8x + 13) / (x - 1) = 2x² - 3x - 13

Now we can factor the quadratic polynomial by using the quadratic formula or by trial and error:

2x² - 3x - 13 = (2x + 5)(x - 3)

Setting each factor equal to zero, we get: 2x + 5 = 0 x = -5/2

x - 3 = 0 x = 3

Therefore, the solutions for the equation (x+1)(2x³ - 5x² - 8x + 13) = 0 are x = -1, x = -5/2, and x = 3.