We know these things about a polynomial function, \(f(x)\): 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 \(f(x)\) given this information.
Mai graphs a polynomial function, \(f(x)\), 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 \(x=3\).
State the degree and end behavior of \(f(x)=2x^3-3x^5-x^2+1\). Explain or show your reasoning.
Is this the graph of \(g(x)=(x-1)^2(x+2)\) or \(h(x)=(x-1)(x+2)^2\)? Explain how you know.
Kiran thinks he knows one of the linear factors of \(P(x)=x^3 + x^2 - 17 x + 15 \). After finding that \(P(3)=0\), Kiran suspects that \(x-3\) is a factor of \(P(x)\), so he sets up a diagram to check. Here is the diagram he made to check his reasoning, but he set it up incorrectly. What went wrong?
The polynomial function \(B(x)=x^3+8x^2+5x-14\) has a known factor of \((x+2)\). Rewrite \(B(x)\) as a product of linear factors.