Question

assignment 5.3 graphs of polynomial functions
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assignment 5.3 graphs of polynomial functions
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question 1
given the function $f(x)=(x - 5)(-10x + 2)^2(x - 1)^3$,
its zeros are (enter exact values in any order separated by commas)
and their multiplicities are (enter values in any order separated by commas)
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Explanation:

Step1: Find the zeros

Set each factor equal to zero.
For $x - 5=0$, we get $x = 5$.
For $-10x + 2=0$, solving gives $x=\frac{1}{5}$.
For $x - 1=0$, we get $x = 1$.

Step2: Determine the multiplicities

The exponent of the factor $(x - 5)$ is 1, so its multiplicity is 1.
The exponent of the factor $(-10x + 2)$ is 2, so its multiplicity is 2.
The exponent of the factor $(x - 1)$ is 3, so its multiplicity is 3.

Answer:

Zeros: $5,\frac{1}{5},1$
Multiplicities: $1,2,3$