At which root does the graph of f of x is equal to open paren x plus 4 close paren to the 6th power times open paren x plus 7 close paren to the 5th power cross the x -axis?

The x-intercepts occur where a factor equals zero: x + 4 = 0 gives x = −4, and x + 7 = 0 gives x = −7. A graph crosses the x-axis at a root with odd multiplicity; the factor (x + 7)⁵ has odd multiplicity, while (x + 4)⁶ has even multiplicity and only touches the axis. Therefore, the graph crosses at negative 7, choice D.

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