Question
For the following factored polynomial, find all of the zeroes and their multiplicities.
Ask by Huang Rowe. in the United States
Jan 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The zeroes and their multiplicities are:
-
with multiplicity 6 -
with multiplicity 2 -
with multiplicity 3
Solution
The given polynomial is:
To find the zeroes and their multiplicities, we examine each factor:
-
: - Zero:
- Multiplicity: 3
- Zero:
-
: - Zero:
- Multiplicity: 2
- Zero:
-
: - Zero:
- Multiplicity: 6
- Zero:
Therefore, the zeroes of the polynomial
-
with multiplicity 6 -
with multiplicity 2 -
with multiplicity 3
Among the provided options, the second one correctly lists all zeroes with their respective multiplicities.
Correct Answer:
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The zeroes of the polynomial
In the world of polynomials, zeroes (or roots) and their multiplicities play a crucial role! They tell us where the polynomial hits the x-axis. In this case,
When calculating zeroes from factored polynomials, a common pitfall is mistaking the signs or miscounting multiplicities! Always double-check the factors you’re examining, as mixing up values can lead to incorrect conclusions. Remember, each factor corresponds to a unique zero which you find by isolating the variable. Happy factoring!
