Algebra 83 - Polynomials | Summary and Q&A

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May 28, 2020
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Algebra 83 - Polynomials

TL;DR

Polynomial functions are powerful mathematical tools that model real world problems and can be used in physics, economics, and social science.

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Questions & Answers

Q: What are examples of real world problems that polynomial functions can model?

Polynomial functions can be used to model problems in physics, economics, and social science. For example, they can be used to model projectile motion, economic growth, or population growth.

Q: What is the difference between a monomial, binomial, and trinomial?

A monomial is a polynomial with only one term, a binomial has two terms, and a trinomial has three terms. The names correspond to the number of terms in the polynomial.

Q: Can the exponents in a polynomial be negative or fractional?

No, the exponents in a polynomial must be non-negative integers. Negative exponents represent division (such as 1/x) and fractional exponents represent roots (such as square root or cube root).

Q: How can a polynomial expression be represented in general notation?

In general notation, the leading term is written as "a sub n" times "x to the nth power", followed by terms with decreasing exponents. The constants, represented as "a sub n", can be positive, negative, or zero.

Summary & Key Takeaways

  • Polynomial functions are a type of function that can model various real world problems.

  • The terms in a polynomial function are called monomials, which are a single term containing variables and coefficients.

  • Polynomials are ordered so that the exponents decrease from left to right, and the leading term determines the degree of the polynomial.

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