- Intro to the Polynomial Remainder Theorem
- Remainder theorem: finding remainder from equation
- Remainder theorem examples
- Remainder theorem
- Remainder theorem: checking factors
- Remainder theorem: finding coefficients
- Remainder theorem and factors
- Proof of the Polynomial Remainder Theorem
- Polynomial division: FAQ
Frequently asked questions about polynomial division
Why might we divide polynomials?
We divide polynomials for the same reason we divide numbers: to solve problems. By breaking a polynomial down into smaller, more manageable pieces, we can solve problems more easily.
Why do we need to know how to divide quadratics specifically?
Quadratics are a very common type of polynomial, so they come up often in problems. Knowing how to divide them by linear factors (like or ) can help us factor them completely.
How do we use the Polynomial Remainder Theorem?
The Polynomial Remainder Theorem tells us that if we divide a polynomial by a linear factor, the remainder will be equal to the polynomial evaluated at a certain value. So if we want to know what the remainder is when we divide a polynomial by , we can just plug in to the polynomial and find out.
Where do these topics come up in the real world?
Polynomials are used in a variety of disciplines, from engineering to physics to economics. Factoring polynomials allows us to work with them in a simpler form, which can make calculations and predictions easier.
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