The equation that describes the zeroes of the graph of function[tex]f(x) = -x^5 + 9x^4-18x^3[/tex] is [tex]f(x) = -x^3(x - 3) (x-6)[/tex]
The function is given as:
[tex]f(x) = -x^5 + 9x^4-18x^3[/tex]
Factor out -x^3
[tex]f(x) = -x^3(x^2 - 9x+18)[/tex]
Expand the expression in the bracket
[tex]f(x) = -x^3(x^2 - 6x - 3x+18)[/tex]
Factorize the expression in the bracket
[tex]f(x) = -x^3(x(x - 6) - 3(x-6))[/tex]
Factor out x - 6
[tex]f(x) = -x^3((x - 3) (x-6))[/tex]
Rewrite the above equation as:
[tex]f(x) = -x^3(x - 3) (x-6)[/tex]
Hence, the equation that describes the zeroes of the graph of function[tex]f(x) = -x^5 + 9x^4-18x^3[/tex] is [tex]f(x) = -x^3(x - 3) (x-6)[/tex]
Read more about zeroes of functions at:
https://brainly.com/question/11514041
