Question 1116233
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9th degree polynomial with a positive leading coefficient; quadruple root at x = -1; double root at x = 0; and triple root at x = 4.  So<br>
(1) function value is negative for large negative values of x;
(2) quadruple root (even degree) at x=-1, so the graph touches the x-axis there but the function value then remains negative;
(3) double root (again even degree) at x=0, so again the graph touches the x-axis there and then the function value again remains negative;
(4) triple root (odd degree) at x=4, so the graph crosses the x-axis there and the function value becomes positive<br>
There are no roots larger than x=4, so the function value then remains positive to the right of that point.<br>
The graph...<br>
{{{graph(400,400,-2,6,-50,50,6x^2(x-4)^3(x+1)^4)}}}