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

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

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

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.