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