Answer:
[tex]f(x)=x^3-9x^2+8x+60[/tex]
Step-by-step explanation:
The zeros of a function are the x-values when f(x) = 0.
Factor Theorem
If f(x) is a polynomial, and f(a) = 0, then (x – a) is a factor of f(x).
If the zeros of the polynomial are -2, 5 and 6 then (x + 2), (x - 5) and (x - 6) are factors of the polynomial.
Therefore, the polynomial in factored form is:
[tex]f(x)=a(x+2)(x-5)(x-6)[/tex]
where a is the leading coefficient.
Given a = 1:
[tex]f(x)=(x+2)(x-5)(x-6)[/tex]
Expand the parentheses to express the polynomial in standard form:
[tex]f(x)=(x+2)(x-5)(x-6)[/tex]
[tex]f(x)=(x^2-3x-10)(x-6)[/tex]
[tex]f(x)=x^3-6x^2-3x^2+18x-10x+60[/tex]
[tex]f(x)=x^3-9x^2+8x+60[/tex]
