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sergey [27]
2 years ago
10

how can you determine that the polynomial function does not have any zeros with even Multiplicity? Explain.​

Mathematics
1 answer:
quester [9]2 years ago
3 0

Answer:

See Below.

Step-by-step explanation:

Remember multiplicity rules:

  • If a factor has an odd multiplicity (e.g. 1, 3, 5...), then the graph will cross the x-axis at that point.
  • If a factor has an even multiplicity (e.g. 2, 4, 6...), then the graph will bounce off the x-axis at that point.

From the graph, we can see that at our zeros, the graph always passes through the x-axis.

Hence, we do not have any zeros with even multiplicity since the graph does not "bounce" at any of the zeros.

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Option b: 2y^{3} +5y^{2} -5y

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Explanation:

The highest degree of a polynomial is the largest exponent of that variable.

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Option a: 4x^{3} -\frac{2}{x}

From the expression 4x^{3} -\frac{2}{x}, the highest degree of the polynomial is 3.

Hence, 4x^{3} -\frac{2}{x} is a polynomial with a degree of 3.

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Option b: 2y^{3} +5y^{2} -5y

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Hence, 2y^{3} +5y^{2} -5y is a polynomial with a degree of 3.

Hence, Option b is the correct answer.

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Hence, Option c is the correct answer.

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