Advanced Algebra w/Trig NAME ______
Quiz Review : Ch 3.1-3.4
1) At most, how many roots could the polynomial have? ____ At most how many turning points? _____
2) Divide by using synthetic division.
3) Use the Remainder Theorem to find if .
4) Without graphing find all the roots of . Use the Rational Zero Theorem to help you find your first zero.
5) Write the polynomial of least degree for the roots of 2, and 5.
6) Determineend behavior of the graph of
7) Find the x-intercepts of , state their multiplicity and sketch the graph.
8) List all possible rational zeros of .
9) Name all of the zeros of ? Use Rational Zero Theorem to find a zero.
10) If P is a polynomial and a is a number for which , circle all of the following statements that are 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.
e) is a factor of Pf) is an intercept of the graph of P.
g) is an x-intercept of P(x). h) there is no reminder if we do synthetic division by a
11) You are given two synthetic divisions of function
3 1 -1 -11 153 6 -15
1 2 -5 0 / -2 1 -1 -11 15
-2 6 10
1 -3 -5 25
True – False?
is divisible by x-3 ______
is divisible by x+2 ______
______ ______
3 is a root of ______, -2 is a root of ______
is a 4th degree polynomial ______
Answer following questions:
What is the quotient when is divided by (x-3)? ______
What would be the answer for (x+2)? ______
Write as a multiplication: = (x-3) ______
12) Find the reduced polynomial of if is a known factor.
13) Determine if is a factor of:.
14) Sketch the graph of
Zeros and multiplicity:______
Degree:______Maximum number of turning Points:______
End Behavior:______
15) Find all the zeros of the polynomial functions and write the polynomial as a product of linear factors.
16) Use the given zero to find the remaining zeros.
17) Find a polynomial function of lowest degree with integer coefficients that has the given zeros.
Zeros: 3+3i, 7
18) Circle all the polynomials: