Answer:
[tex]F(x)=(x-11)(x-3)[/tex]
Step-by-step explanation:
we have
[tex]F(x)=x^{2} -14x+33[/tex]
Find the zeros of the function
F(x)=0
[tex]0=x^{2} -14x+33[/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]-33=x^{2} -14x[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side
[tex]-33+49=x^{2} -14x+49[/tex]
[tex]16=x^{2} -14x+49[/tex]
Rewrite as perfect squares
[tex]16=(x-7)^{2}[/tex]
square root both sides
[tex](x-7)=(+/-)4[/tex]
[tex]x=(+/-)4+7[/tex]
[tex]x=(+)4+7=11[/tex]
[tex]x=(-)4+7=3[/tex]
so
The factors are
(x-11) and (x-3)
therefore
[tex]F(x)=(x-11)(x-3)[/tex]
