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### Course: Algebra 2 > Unit 4

Lesson 4: Polynomial Remainder Theorem- 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

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# Intro to the Polynomial Remainder Theorem

The Polynomial Remainder Theorem allows us to determine whether a linear expression is a factor of a polynomial expression easily. It tells us the remainder when a polynomial is divided by
\[x - a\] is
\[f(a)\]. This means if
\[x - a\] is a factor of the polynomial, the remainder is zero. It's a neat trick to quickly find remainders without doing long division!

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