Which of the following graphs could represent a 6th-degree polynomial function, with 3 distinct zeros, 1 zero with a multiplicity of 2, 1 zero with a multiplicity of 3, and a negative leading coefficient?
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A 6th degree poly should give you 6 zeros.
Of these 6, 3 must be distinct. This means you'll have exactly 3 points on the horizontal number like where the graph either crosses or touches the horizontal axis.
If a zero has a multiplicity of 2, that means the graph will loop either up or down and that its vertex will only touch (not cross) the horiz. axis.
If ... a multiplicity of 3, the graph will actually cross the horiz axis at that x-value.
Could you possibly post illustrations of the four graphs that represent possible answers?