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We know these things about a polynomial function, \(f\): It has exactly one relative maximum and one relative minimum, it has exactly three zeros, and it has a known factor of \((x-4)\). Sketch a graph of \(f\) given this information.
Mai graphs a polynomial function that has three linear factors \((x+6)\), \((x+2)\), and \((x-1)\). But she makes a mistake. What is her mistake?
Here is the graph of a polynomial function with degree 4.
Select all of the statements that are true about the function.
The leading coefficient is positive.
The constant term is negative.
It has 2 relative maximums.
It has 4 linear factors.
One of the factors is \((x-1)\).
One of the zeros is \(x=2\).
There is a relative minimum between \(x=1\) and \(x=3\).
Is this the graph of \(g(x)=(x-1)^2(x+2)\) or \(h(x)=(x-1)(x+2)^2\)? Explain how you know.