Zeros of polynomials (multiplicity) | Polynomial graphs | Algebra 2 | Khan Academy | Summary and Q&A

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July 19, 2019
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Zeros of polynomials (multiplicity) | Polynomial graphs | Algebra 2 | Khan Academy

TL;DR

Learn how to determine the factors of a polynomial by analyzing the roots and exponents in factored form.

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Questions & Answers

Q: Why is factored form useful in analyzing polynomial roots?

Factored form helps identify the roots, as the x-values that make the polynomial equal to zero can be determined by analyzing the factors.

Q: How does the presence or absence of sign changes affect the exponents in factored form?

Sign changes around a root indicate an odd exponent in the corresponding factor, while the absence of a sign change suggests an even exponent.

Q: How can we determine the correct factors when given multiple-choice options?

By comparing the roots and exponents in the options with the sign changes and expected exponents, the factors consistent with the polynomial's roots can be identified.

Q: How can we determine the factors if the graph touches the x-axis but does not have a sign change?

If there is no sign change, the exponent in the corresponding factor should be even, as the graph only touches the x-axis briefly before returning to its initial direction.

Summary & Key Takeaways

  • Factored form of a polynomial is useful for determining its roots, which are the x-values that make the polynomial equal to zero.

  • The odd or even exponents in the factors of a polynomial depend on the presence or absence of sign changes around the corresponding roots.

  • By analyzing the roots and exponents in multiple-choice options, the correct factors of a polynomial can be identified.

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