Advanced Algebra w/Trig NAME ______
TEST REVIEW : Ch 3 DATE ______PER ______
Show the process to earn credit. If a method is given, you must show that method.
#1-16 Multiple Choice: Write the letter of the BEST answer.
_____ 1) At most, how many roots could the polynomial have?
_____ 2) Divide by using synthetic division.
_____ 3) Use the Remainder Theorem to find if .
_____ 4) Find the complex roots of . Use synthetic division and/or
factoring.
_____ 5) Write the polynomial of least degree for the roots of , , and 5.
_____ 6) Determine the far-left and the far-right end behavior of the graph of
_____ 7) Factor to find all real zeros of .
_____ 8) Find the x-intercepts of and state whether the graph of P
crosses the x-axis or bounces at the zeros.
_____ 9) List all possible rational zeros of .
_____ 10) Name all of the rational zeros of ? Prove your process.
_____ 11) Determine between which consecutive integers the real zeros of
are located. State the reason using the zero location theorem.
a) and 0 b) 0 and 1
c) and d) no real zeros
_____ 12) Find the greatest integer lower-bound of the zeros of .
Show your process!
_____ 13) If P is a polynomial and a is a number for which , which of the following is true?
a) is a factor of P. b) is an intercept of the graph of P.
c) d) a is a zero of the polynomial.
#14-17 Completion.
______14) Divide by .
______15) Find the reduced polynomial of
if is a known factor.
______16) Determine if is a factor of:.
17) Sketch the graph of . Label x- and y-intercepts, maximum and
minimum points, and the graph.
Factor to find the roots.
Use a t-chart of values to plot points.
Find all the zeros of the polynomial functions and write the polynomial as a product of linear factors.
18)
Use the given zero to find the remaining zeros.
19)
Find a polynomial function of lowest degree with integer coefficients that has the given zeros.
20) Zeros:
Find a polynomial function of lowest degree with integer coefficients that has the given zeros.
21) Zeros: 3+3i, 7