Exploring Polynomial Functions and Roots

The rational roots of the polynomial $$f(x) = x^3 - 6x^2 + 11x - 6$$ are (a)   . Write your answers from least to greatest.

Perform synthetic division on the polynomial $$f(x) = 2x^3 - 3x^2 + 4x - 5$$ by $$x - 1$$ . What is the remainder?

Factor the polynomial $$2x^2-9x-35$$ .

Solve the equation $$x^2 - 4x - 5 = 0$$ . Put your answers in least to greatest order.

x=​ (a)   ​ (b)  

Analyze the behavior of the polynomial $$f(x) = x^3 - 3x^2 + 2x$$ . What is the end behavior as $$x \to \infty$$ ?

Match equation with its possible rational roots.

Plot where the roots of the graph are located.

In the above graph complete the following end behavior:

As x --> ∞, f(x) --> ​ (a)  

As x --> - ∞, f(x) -->​ (b)  

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Cam divided (x⁴ + 3x² - 4x - 2) by factor of (x-2) using synthetic division. His work is shown above. Which best describes his mistake?

Is 9 a possible rational zero of the equation? Why or why not?

p(x)= x³ - 6x² - x + 30