Polynomial Algebra Worksheets
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1
2(1) Write each polynomial in factored form. Then sketch its graph, state its degree, and list its roots.
(
) (
)
(a)
(b)
(c)
DEGREE:
DEGREE:
DEGREE:
ROOTS:
ROOTS:
ROOTS:
(2) Consider the degree of each function above. Then consider each original equation.
(a) How is the degree related to
the function in standard form?
____________________________________________________
(b) How is the degree related to
the function in factored form?
____________________________________________________
(c) How is the degree related to
the function’s number of roots?
____________________________________________________
(3) State the degree of each function. Then determine how many roots are real and complex.
(a)
(b)
(c)
(d)
y
y
y
y
x
x
x
x
DEGREE:
DEGREE:
DEGREE:
DEGREE:
# OF REAL ROOTS:
# OF REAL ROOTS:
# OF REAL ROOTS:
# OF REAL ROOTS:
# OF COMPLEX ROOTS:
# OF COMPLEX ROOTS:
# OF COMPLEX ROOTS:
# OF COMPLEX ROOTS:
(4) Consider the graph of the equation
.
(a) Graph the equation in your calculator.
Sketch it on the axes at right.
(b) Check the graph carefully. What seems strange about
where the graph has a “through slowly” point?
______________________________________________
(c) How many real roots must the graph have? ______
How many must be complex? ______
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