Respuesta :
The equation of the polynomial is -
f(x) = [tex]x^{3} - 16x^{2} -41x+840[/tex].
We have a polynomial function whose graph intercepts the horizontal axis at -7, 8, and 15.
We have to identify the polynomial.
What is Polynomial ?
A polynomial is an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).
According to the question -
x = -7, 8, 15 are the horizontal or the x - axis intercepts of the graph of the polynomial.
This means for -
x = -7
x = 8
x = 15
the polynomial (say f(x)) is equal to 0.
Therefore, x = -7 , x = 8 and x = 15 are the solutions of the polynomial f(x).
Then -
(x + 7) , (x - 8) and (x - 15) are the factors of this polynomial. Therefore -
f(x) = (x + 7)(x - 8)(x - 15)
f(x) = [tex](x^{2} -x-56)(x-15)\\[/tex]
f(x) = [tex]x^{3} - 16x^{2} -41x+840[/tex]
Hence, the equation of the polynomial is -
f(x) = [tex]x^{3} - 16x^{2} -41x+840[/tex]
To solve more questions on Polynomials, visit the link below-
https://brainly.com/question/12404751
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