Answer:
(x-9)(x-3)
Step-by-step explanation:
multiply -9 and -3 to get 27, add to get -12
Using the Factor Theorem, it is found that the factored form of the polynomial is (x - 9)(x - 3).
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 equation is:
[tex]x^2 - 12x + 27 = 0[/tex]
Which is a quadratic equation with coefficients a = 1, b = -12, c = 27, hence:
[tex]\Delta = b^2 - 4ac = (-12)^2 - (4)(1)(27) = 36[/tex]
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a} = \frac{12 + \sqrt{36}}{2} = 9[/tex]
[tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a} = \frac{12 - \sqrt{36}}{2} = 3[/tex]
Hence (x - 9)(x - 3).
More can be learned about the Factor Theorem at https://brainly.com/question/24380382
