Respuesta :
Using the Factor Theorem, it is found that the complete factorization of the expression is given by:
[tex]x^2 - 14x + 48 = (x - 6)(x - 8)[/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]
In which a is the leading coefficient.
In this problem, the expression is given by:
[tex]x^2 - 14x + 48[/tex]
We factor it according to it's roots, that is:
[tex]x^2 - 14x + 48 = 0[/tex]
Which is a quadratic equation with coefficients a = 1, b = -14 and c = 48, hence:
[tex]\Delta = (14)^2 - 4(1)(48) = 4[/tex]
[tex]x_{1} = \frac{14 + \sqrt{4}}{2} = 8[/tex]
[tex]x_{2} = \frac{14 - \sqrt{4}}{2} = 6[/tex]
Hence the complete factorization of the expression is given by:
[tex]x^2 - 14x + 48 = (x - 6)(x - 8)[/tex]
More can be learned about the Factor Theorem at https://brainly.com/question/24380382
