Question

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
muliplicity of 3, and a negative leading coefficient?

Answer 1

6th-degree polynomial: the degree is even, so the ends (at + and - infinity in the x direction) either both go to + infinity or - infinity (both ends go in the same direction)

3 distinct zeros: so it touches/crosses the x-axis 3 times

1 zero with a multiplicity of 2: even multiplicity, so there's one point where the graph touches the x-axis and goes back in the other direction

1 zero with a multiplicity of 3: odd multiplicity, so there's one zero where the graph crosses the x-axis

negative leading coefficient: combined with an even degree, this means the graph goes to - infinity in both directions

with all that info in mind, try to find the matching graph