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Algebra 2
Name: ____________________
HW#7 Fundamental Theorem of Algebra and Graphs of Polynomial Functions
I.
1.
Find the requested information for each polynomial graph. All polynomials are in standard form.
P  x   4 x 4  3x3  x 2  4
2.
P  x   2 x 7  6 x5  2 x 3
Leading Coefficient: _________
Leading Coefficient: _________
Degree: _________
Degree: _________
y -intercept: _________
y -intercept: _________
Total Number of Roots: _________
Total Number of Roots: _________
End Behavior:
End Behavior:
x  , y  __________
x  , y  __________
x  , y  __________
x  , y  __________
II.
Sketch a graph of the function WITHOUT using the graphing calculator. Include real zeros on the
graph and the end behavior. Also specify the degree of the polynomial.
5. P  x    x  2 
IV.
8.
2
 x  3  x  1
3
6. P  x    x  2 x  5
2
 x  2
Identify whether the following graphed functions have an odd or even degree and also whether
they have a positive negative leading coefficient. For the real roots, identify whether positive or
negative and their multiplicity.
9.
Odd or Even? ________________
Odd or Even? ________________
 or  Leading Coefficient? ________________
 or  Leading Coefficient? ________________
Real Roots? (  or

AND multiplicity)
Real Roots? (  or

AND multiplicity)
III.
Write a possible equation for a polynomial with the following sketch. Leave your equation in
factored form.
11.
12.
10.
Write the simplest polynomial function (in standard form) with the following zeros.
1. 3i and  5
II.
Solve each equation by finding all the roots (EXACT VALUE). Use the calculator to help you.
2. x  7 x  15 x  9  0
3
2
3. x  3x  5 x  27 x  36
4
3
2