Answer:
The y-intercept of the function is -210 and the x-intercepts of the function are 5,6,7.
Step-by-step explanation:
The given function is
[tex]f(x)=x^3-18x^2+107x-210[/tex]
To find y-intercept put x=0.
[tex]f(x)=(0)^3-18(0)^2+107(0)-210[/tex]
[tex]f(x)=-210[/tex]
The y-intercept of the function is -210.
To find the x intercepts put f(x)=0.
[tex]x^3-18x^2+107x-210=0[/tex]
For x=5, the above equation is true, therefore (x-5) is factor of the equation.
Use synthetic method to find the factors.
[tex](x-5)(x^2-13x+42)=0[/tex]
[tex](x-5)(x^2-6x-7x+42)=0[/tex]
[tex](x-5)(x(x-6)-7(x-6))=0[/tex]
[tex](x-5)(x-6)(x-7)=0[/tex]
Use zero product property and equate each factor equal to zero.
[tex]x=5,6,7[/tex]
Therefore the x-intercepts are 5, 6 and 7.