Suppose f(x)=(x−7)g(x), where g(x) is some polynomial.

Question

Suppose f(x)=(x−7)g(x), where g(x) is some polynomial.

Find a solution: f(x)=0.

x=7

Suppose g(x)=0 has solutions for x=−6, x=2, and no others.

Find the y-intercepts of the graph of y=f(x): __?__

Answer 1

For f(x) = 0, x ∈ {-6, 2, 7}

f(x) = (x - 7)(x + 6)(x - 2)

y-intercept at f(0).