Q:

NEED HELP ASAP PLZ!!Factor completely.x2βˆ’14x+48Enter your answer in the box.

Accepted Solution

A:
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