1. Given the function f(x) =6×5 -2×3 +11×2 +10.
a. Find a5 ,a4 , a3 , a2 , a1 and a0.
b. Write down the leading term of the polynomial.
c. Write down the leading coefficient of the polynomial.
d. State the degree of the polynomial
e. How many x-intercepts does f have?
f. How many turning points does f have?
g. State the extreme behavior of f.
2. Determine whether or not -2 is a zero of . Justify your answer.
3. Determine whether or not 3 is a zero of . Justify your answer.
4. Find the zeros of .
5. Find the zeros of .
6. Let .
a. Find the zeros of f(x) and their multiplicities.
b. Determine the behavior of the graph at each zero. (Does the graph cross or touch the x-axis at the zero?)
c. Find the leading term.
d. State the degree of the polynomial.
e. State the leading coefficient.
f. State the end behavior of the graph.
g. Sketch (draw) the graph.
7. Let f(x) = = 3x(x – 2)3(2x + 1)(x + 3)2.
a. Find the zeros of f(x) and their multiplicities.
b. Determine the behavior of the graph at each zero. (Does the graph cross or touch the x-axis at the zero?)
c. Find the leading term.
d. State the degree of the polynomial.
e. State the leading coefficient.
f. State the end behavior of the graph.
g. Sketch (draw) the graph.
8. Develop an appropriate formula for the polynomial function of minimum degree, f(x), whose graph is shown below.
