Question

Given the function f(x) = x3 − 18x2 + 107x − 210, what are the y-intercept and x-intercepts? Show the work steps to find these intercepts

Answer 1

The y-intercept of the function is -210 and the x-intercepts of the function are 5,6,7.

Explanation:

The given function is

`f(x)=x^3-18x^2+107x-210`

To find y-intercept put x=0.

`f(x)=(0)^3-18(0)^2+107(0)-210`

`f(x)=-210`

The y-intercept of the function is -210.

To find the x intercepts put f(x)=0.

`x^3-18x^2+107x-210=0`

For x=5, the above equation is true, therefore (x-5) is factor of the equation.

Use synthetic method to find the factors.

`(x-5)(x^2-13x+42)=0`

`(x-5)(x^2-6x-7x+42)=0`

`(x-5)(x(x-6)-7(x-6))=0`

`(x-5)(x-6)(x-7)=0`

Use zero product property and equate each factor equal to zero.

`x=5,6,7`

Therefore the x-intercepts are 5, 6 and 7.