Solutions to problem set: Dr. Cruzan Web: Polynomial Functions - Grouping
1. f(x) = 2x4 - 6x3 - 4x + 12
group
group
A new common factor
Be careful
with signs.
Note: The fundamental theorem of algebra says
that this function should have four roots.
There are actually three cube roots of 2;
Two of those have non-zero imaginary parts.
2. f(x) = x4 - 2x3 - 8x + 16
group
group
3. f(x) = x4 - 9x3 - 4x2 + 36x
Note: We could also
have taken out the GCF
of x first (probably
should have!), but the
result is the same.
4. f(x) = - 3x4 + 3x2 - 2x2 + 2x
group
© J. Cruzan 2013
Solutions to Web Problems: Polynomial zeros by grouping
group
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Solutions to problem set: Dr. Cruzan Web: Polynomial Functions - Grouping
3
2
5.
f(x) = - 8x + 56x + x - 7
6.
f(x) = 3x - 12x - 2x + 8x
4
3
2
Note: Whenever a GCF contains
the independent variable (x), zero
is a root of the function.
7.
3
Roots are also called “zeros”.
They mean the same thing.
2
f(x) = 7x + 28x + x + 4
Here I‛ve “rationalized”
the denominator.
8. f(x) = x6 + 2x5 - 4x2 - 8x
The fund. thm. of alg. says
that there are actually four
1/4th roots of 4. They are
±2 and two roots with nonzero imaginary parts.
© J. Cruzan 2013
Solutions to Web Problems: Polynomial zeros by grouping
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