Respuesta :
Using the Factor Theorem, it is found that the correct factorization of [tex]x^2 - x - 2[/tex] is:
[tex]x^2 - x - 2 = (x + 1)(x - 2)[/tex]
What is the Factor Theorem?
The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
a is the leading coefficient.
In this problem, the polynomial is:
[tex]x^2 - x - 2 = 0[/tex]
Which is a quadratic equation with coefficients [tex]a = 1, b = -1, c = -2[/tex], then:
[tex]\Delta = b^2 - 4ac = (-1)^2 - 4(1)(-2) = 9[/tex]
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a} = \frac{1 + 3}{2} = 2[/tex]
[tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a} = \frac{1 - 3}{2} = -1[/tex]
Hence, the factorization is:
[tex]x^2 - x - 2 = (x + 1)(x - 2)[/tex]
To learn more about the Factor Theorem, you can take a look at https://brainly.com/question/24380382
