An equation for a polynomial function with given intercepts is
[tex]P(x)=x^3-16x^2-41x+840[/tex]
Given :
The intercepts at the horizontal axis at -7, 8, and 15.
so, the x intercepts are -7, 8, and 15.
Lets write the x intercepts in factor form
if 'a' is x intercept then (x-a) is a factor
x intercepts are -7, 8, and 15.
the factors are
[tex](x-(-7)) (x-8)(x-15)\\(x+7)(x-8)(x-15)[/tex]
Now to write the polynomial we multiply all the factors
[tex]P(x)=(x+7)(x-8)(x-15)\\P(x)=\left(x^2-x-56\right)\left(x-15\right)\\P(x)=x^3-16x^2-41x+840[/tex]
Learn more : brainly.com/question/18537685
