The function of the polynomial graph when factored is (d) [tex]f(x) = x^3 - 8x^2+ 21x - 18[/tex]
From the question (see attachment), we have the following highlights:
- The graph crosses the x-axis at x = 2.
- The graph touches the x-axis at x = 3
This means that:
- The graph has a multiplicity of 1 at x = 2
- The graph has a multiplicity of 2 at x = 3
So, the function of the graph is:
[tex]f(x) = (x - 2)(x - 3)^2[/tex]
Expand the exponent
[tex]f(x) = (x - 2)(x^2 - 6x + 9)[/tex]
Expand
[tex]f(x) = x^3 - 6x^2 + 9x - 2x^2 + 12x - 18[/tex]
Collect like terms
[tex]f(x) = x^3 - 6x^2 - 2x^2+ 9x + 12x - 18[/tex]
[tex]f(x) = x^3 - 8x^2+ 21x - 18[/tex]
Hence, the function of the graph is (d)
Read more about polynomial functions at:
https://brainly.com/question/2833285
