The function f(x) = x3 – 8x2 + x + 42 has zeros located at 7, –2, 3. Verify the zeros of f(x) and explain how you verified them. Describe the end behavior of the function.

Step-by-step explanation:

At first you need to turn roots into factors and then multiply the

then you have

f(x) = a(x + 2)(x -5)^2

f(x) = a(x + 2)(x^2 - 10x + 25)

f(x) = a(x^3 - 8x^2 + 5x + 50)

You can use either synthetical or the factor

theorem

f(-2) = a(-8 - 8(4) + 5(-2) + 50) = a(0) = 0.. check, f

=-2

€(5) = a(125 - 8(25) + 5(5) + 50) = a(0) = 0 check, f

= 5 works

Then divide it to the the second multi

And you should get x^2 - 3x - 10 = (x - 5)(x + 2),

where the other two zeros are X =5 , and x=-2