ANSWER
The graph of
[tex]f(x) = {(x + 4)}^{6} {(x + 7)}^{5} [/tex]
crosses the x-axis at
[tex]x = - 7[/tex]
EXPLANATION
The nature of the multiplicity of a given polynomial function determines whether the graph crosses the x-axis at that intercept or not?
[tex]f(x) = {(x + 4)}^{6} {(x + 7)}^{5} [/tex]
If the multiplicity of the factor is even as in
[tex] {(x + 4)}^{6} [/tex]
the graph touches but does not cross the x-axis at the intercept where
[tex]x = - 4[/tex]
This means that the x-axis is a tangent to the function at this point.
However, if the multiplicity is odd, as in
[tex] ({x + 7})^{5} [/tex]
the graph crosses the x-axis at the intercept where
[tex]x = - 7[/tex]
